Sponsers. NPDE program LATEST ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS. Conference on. December 15 17, 2016

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1 Conference on LATEST ADVANCES IN COMPUTATIONAL AND APPLIED MATHEMATICS December 15 17, 2016 Mahindra-École Centrale (MEC), Hyderabad, India Sponsers NPDE program

2 COMMITTEE CONTACT ORGANIZERS Nagaiah Chamakuri MEC, Hyderabad B. V. Rathish Kumar IIT Kanpur Sashi Kumar Ganesan IISc Bangalore INVITED SPEAKERS Prof. Amiya K. Pani (IIT Bombay) Prof. S. Sundar (IIT Madras) Prof. M. K. Kadalbajoo (IIT Kanpur) Prof. G.D. Veerappa Gowda (TIFR CAM, Bangalore) Prof. A.S. Vasudeva Murthy (TIFR CAM) Prof. A.K. Nandakumaran (IISc, Bangalore) Prof. G.P. Rajasekhar (IIT Kharagpur) Prof. Y.V.S.S. Sanyasiraju ( IIT Madras) Prof. Miha Ravnik (University of Ljubljana, Slovenia) Prof. Swaroop Nandan Bora (IIT Guwahati) Prof. Sitabra Sinha (IMSC Chennai) Prof. Pranay Goel (IISER Pune) Prof. C. Vijaysekhar (MEC, Hyderabad) Prof. A. K. Battacharya (MEC, Hyderabad) Dr. M. Naresh (NRSC, ISRO, Hyderabad) Prof. Somanchi K Murthy (DIAT, Pune) 2

3 COMMITTEE CONTACT CONFERENCE ADVISORY COMMITTEE Prof. K. Kunisch (University of Graz, Austria) Prof. G. Warnecke (University of Magdeburg, Germany) Prof. A. K. Pani (IIT Bombay) Prof. S. Sundar (IIT Madras) Prof. G. D. Veerappa Gowda (TIFR CAM, Bangalore) Prof. A.K. Nandakumaran (IISc, Bangalore) Prof. G.P. Rajasekhar (IIT Kharagpur) Prof. B.V. Rathish Kumar (IIT Kanpur) Prof. Sashi Kumar Ganesan (IISC Bangalore) Prof. Nagaiah Chamakuri (MEC, Hyderabad) LOCAL ORGANIZING COMMITTEE Dr. Ch. Nagaiah (MEC, Hyderabd) Dr. Ch. Satyanarayana (MEC, Hyderabad) Dr. J. Mahipal (MEC, Hyderabad) Dr. Jayasri (MEC, Hyderabad) Dr. Jay Prakash (MEC, Hyderabad) Dr. Manoj Kumar (MEC, Hyderabad) Dr. Madhukanth Sharma (MEC, Hyderabad) Dr. Sanjuktha Das (MEC, Hyderabad) 3

4 COMMITTEE CONTACT CONTACT Prof. Nagaiah Chamakuri Mahindra École Centrale (MEC), Hyderabad, Telangana, , India. Tel LOCATION Mahindra École Centrale (MEC) Tech Mahindra Technology Centre, Survey No: 62/1A, Bahadurpally, Jeedimetla, Hyderabad, Telangana, , India. Tel

5 WELCOME DEAR PARTICIPANT, The purpose of this conference is to bring together experts in the field of computational mathematics, to share their ideas that focus on various theoretical and computational aspects, to foster learning and inspiration, and to provoke discussions and exchanges on the state-of-the-art in Applied Mathematics. Specifically, numerical analysis of modern methods for PDEs, developing efficient and robust methods for solving PDEs, optimization and optimal control, high performance computing, applications of PDEs in the natural and engineering sciences. These include but are not limited to computational scientists, engineers and last but not least researchers from industry. We wish you a fruitful and stimulating time at the conference, and hope you will enjoy your stay in Hyderabad! The organizing commitee 5

6 CONTENTS CONTENTS COMMITTEE CONTACT 2 WELCOME 5 SCHEDULE 7 ABSTRACTS 10 ARRIVAL AND MEALS 47 PARTICIPANTS 48 6

7 SCHEDULE SCHEDULE THURSDAY, DECEMBER 15 8:20-9:00 Registration Opening :15 Rathish Kumar (Keynote Speaker) 10:15 10:40 Coffee break Scientific Computing: A New Way of Looking at Mathematics 10: G.P.Rajasekhar Boundary element methods for viscous flows 11: Miha Ravnik Passive and active nematic microfluidics Lunch 13: Y.V.S.S.S. Raju Finite Difference type Computations using Radial Basis Functions (RBF) 14: Pranay Goel Coarse-grained models of multiscale calcium and electrical activity in the pancreas 15:00 15:30 Coffee break 15: Gande Naga Raju A new smoothness indicator for third-order WENO scheme 15: Birupaksha Pal A variational multiscale scheme for incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian setup 16:10 16:30 Victor Methoro Job Polynomial Pressure Projection Stabilized (PPPS) FEM with an Application to Nanofluid Heat Transfer 16: Anjanna Matta Double-diffusive Hadley-Prats flow in a horizontal porous layer with a concentration based internal heat source 16: Kiran Kumar A high order numerical scheme for solving nonlinear singular boundary value problems 17: Manoj Kumar Yadav Multi-time step domain decomposition method 17: Naddi Shankaraiah Phase-ordering kinetics in martensitic triple-well model Landau free energies 17: Jayasri D Liquid Crystals confined to restricted geometries: A Monte Carlo Study 18:30 Dinner 7

8 SCHEDULE SCHEDULE FRIDAY, DECEMBER 16 Special theme talks on the frontiers on Numerical Analysis and Applications :45 G. D. V. Gowda Applications of Hamilton-Jacobi equations in Shape from Shading :30 Kadalbajoo Numerical methods for Partial-integral differential equations (PIDEs) arising in finance: An Overview 10:30 10:50 Coffee break 10: Sashi Kumaar G Finite element methods for PDEs with moving boundaries 11: M. Naresh Dynamic Models for Infectious Diseases Lunch 13: S. Sundar Finite Pointset Method - Some Important Issues 14: C. Vijaysekhar Pricing, Hedging, and Risk: A Tutorial 15:00 15:30 Coffee break 15: Debashish Pradhan On the Convergence Rate of a Robin-Type Non-Overlapping Domain Decomposition Procedure for Second Order Parabolic Problems 15:50 16:10 Arumugam Gurusamy Finite Element Method for Keller-Segel Chemotaxis System 16:10 16:30 V. Subburayan Uniformly convergent FD scheme for singularly perturbed system of convection-diffusion type delay differential equations 16: Mahipal Jetta Fourth Order Nonlinear Diffusion Filters for Image Denoising 16: V. Dhanya Varma Numerical solution of heat and mass transfer in fluidized beds using DG methods 17: Madhukant Sharma Solutions to fractional functional differential equations in a banach space 17: Madhavi Latha An order level inventory model under l 2-system with quadratic demand with k-release rule 18:30 Conference dinner 8

9 SCHEDULE SCHEDULE SATURDAY, DECEMBER 17 Special theme talks on the frontiers on Numerical Analysis and Applications :45 A.K.Nandakumaran Ray, Radon, Fourier Transforms and Inverse Problem in Image Reconstruction :30 A.S.Vasudeva Murthy 10:30 10:50 Coffee break Far field boundary conditions and their approximation 10: Sitabhra Sinha Modeling the activity of the entire primate brain: A meso-scale dynamical perspective 11: Arya Kumar B Optimal Paths for Missile-Target pursuit using Differential Evolution Lunch 13: Somanchi Murthy Finite Element Study of Mixed Convection Process in a Concentration Stratied Fluid Saturated Porous Enclosure 14: N. Balasubramani Constrained Rational Quartic Fractal Interpolation Surface 14: Prasad Pokkunuri Impulse Response of the Viscous Burger s Equation with a Magneto-Rheological Viscosity 14:55 15:15 Ch. Satyanarayana RBF based grid free local scheme with an optimal shape parameter 15:15 15:35 Samala Rathan Seventh-order WENO scheme with the L 1-norm type smoothness indicators 15: Jai Prakash Formation of a stable ring of bubbles in a Couette device with Taylor vortices 16:00 Coffee break & Departure 9

10 Scientific Computing: A New Way of Looking at Mathematics Amiya Kumar Pani Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, India Abstract In this workshop talk, I plan to provide some answers to the following questions: Why there is a need to relook at Mathematics? In what way questions asked in traditional Mathematics are different in the new frame? What are its major objectives or emphasis? Does it answer the major concern of the user community like How does one believe the numbers that are crunched by the machine? Does it preserve the aesthetic beauty of the traditional Mathematics? With the help of a toy problem like a finite difference method (FDM) for a Poisson problem in computational PDEs, my focus will be to show how theory of PDE helps to articulate the questions in Computational PDEs and then, discuss some issues like stability, consistency and convergence and their role in answering the questions posed. Finally, I shall conclude my talk on a hard problem related to FDM with some attempts in this direction. 10

11 Boundary element methods for viscous flows G. P. Raja Sekhar Department of Mathematics, Indian Institute of Technology Kharagpur Kharagpur , India Abstract In this talk, we first present boundary element methods (BEM) for problems in potential theory. We show boundary integral formulation for Laplace equation and then introduce the corresponding boundary element method by discretizing the boundary integral equations. We then move to BEM to solve two dimensional Stokes flow problems. In this connection, we investigate steady, pressure-driven, two dimensional flow of Newtonian fluid through slip-patterned, rectangular channels in the low Reynolds number limit. The slip flow regime is modelled using the Navier s slip boundary condition. Based on the characteristic length of the patterning, we have considered two types of slip, namely large and fine. Moreover, depending on the relative location of the top and bottom boundary, in-phase and out-phase conditions are defined. Boundary element method (BEM) is used to numerically solve Stokes equation and obtain the streamline profiles. Streamlines, shear stresses, pressure gradients and velocity profiles are analyzed to gain a proper understanding of the flow mechanics. The talk ends with some remarks on coupled problems. Keywords : Boundary element method, Stokes equation, patterned-slip. 11

12 Passive and active nematic microfluidics Miha Ravnik 1,2 1 University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, 1000 Ljubljana, Slovenia 2Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia Abstract Microfluidics based on complex active and passive nematic fluids gives access to different mechanisms for controlling flow profiles, flow steering, flow mixing and particle transport, all relying on the coupling between the flow and the internal molecular order. Here, we present our modelling study, in collaboration with partner experiments, that explores the coupling between geometry and orientational ordering in active and passive nematic microfluidics. We observe that in simple channels the geometry gets rather directly screened in both the flow and director profile, unless if generating topological defects. In more complex channels and geometries, we observe formation of different topological defects, as generated by the variable flow profiles. The symmetry and topology of defects is shown to be controllable by the geometry of the channel. For active microfluidics, we show that active defects act as local micro-pumps for the material flow. More generally, by designing the orientational profile of active or passive nematic we can control the profile and possibly topology of the material flow. Selected related references [1] S. M. Hashemi, U. Jagodic, M. R. Mozaffari, M. R. Ejtehadi, I. Muševič and M. Ravnik, Fractal Nematic Colloids, accepted in Nature Commun. (2016) [2] J. Aplinc, S. Morris and M. Ravnik, Phys. Rev. Fluids 1, (2016) [3] M. Nikkhou, M. Škarabot, S. Čopar, M. Ravnik, S. Žumer and I. Muševič, Nature Phys. 11, 183 (2015). [4] A. Sengupta, U. Tkalec, M. Ravnik, J.M. Yeomans, C. Bahr, S. Herminghaus, Phys. Rev. Lett. 110, (2013). [5] M. Ravnik and J. M. Yeomans, Phys. Rev. Lett. 110, (2013). 12

13 Coarse-grained models of multiscale calcium and electrical activity in the pancreas Pranay Goel Indian Institute of Science Education and Research(IISER), Pune Abstract We are interested in studying various aspects of electrical activity in the pancreas. Specifically, we have been constructing models of glucosestimulated insulin secretion (GSIS) from the pancreatic islets of Langerhans. GSIS is a complex process that involves not only electrical but also calcium oscillations. Further, calcium is sequestered in spatially complex compartments, which means that the geometry of the problem is of considerable importance in modelling. I will describe our work on constructing homogenized models of these processes, which takes into account the multiscale nature of the problem. 13

14 Applications of Hamilton-Jacobi equations in Shape from Shading G. D. Veerappa Gowda TIFR Centre for Applicable Mathematics, Bangalore INDIA Abstract Hamilton-Jacobi equations have wide applications in numerous fields of science such as classical mechanics and geometrical optics in physics. In this talk we emphasis upon both theoretical and numerical perspectives for this first order non-linear partial differential equations especially focussing on the application in the shape from shading i.e., to recover the shape of 3-dimensional object from 2-dimensional informations. 14

15 Numerical methods for Partial-integral differential equations (PIDEs) arising in finance: An Overview Mohan K Kadalbajoo IIT Kanpur, India Abstract This talk would give a broad overview of popular and current numerical methods for solving PIDEs with particular applications in option pricing problems. 15

16 16 Trapped modes in two-layer fluids with different upper and bottom conditions Swaroop Nandan Bora & Sunanda Saha Department of Mathematics Indian Institute of Technology Guwahati Guwahati , INDIA Trapped waves are of considerable interest in providing examples of discrete wave frequencies in the presence of a continuous spectrum. In this work, we first investigate the existence of trapped modes in a two-layer fluid of finite depth subject to different conditions: (i) upper surface bounded above by a rigid lid; (ii) upper surface bounded above by a thin ice-cover; (iii) fluid flowing over an elastic bottom at a finite depth. In all these problems, a submerged horizontal circular cylinder is placed in either of the layers. The effect of surface tension at the surface of separation is neglected and each fluid layer is considered to be immiscible. Furthermore, the assumptions of linear and time harmonic motions are followed. To solve the ice-cover problem, the standard idealization of ice as a thin elastic plate, which responds to only flexural changes, is followed. In the elastic bottom problem, the flexural bottom is considered as a thin elastic plate and is based on the Euler-Bernoulli beam equation. In this study of trapped waves, mixed boundary value problems are set up for the determination of velocity potentials corresponding to each layer where the governing partial differential equation happens to be modified Helmholtz equation in two-dimensions for oblique incidence within the fluid. The governing equation is accompanied by boundary conditions near the upper rigid boundary or the ice-cover surface or the free surface, at the interface between two fluids and at the bottom boundary, if any, depending on the problem considered. The trapped mode condition arises which ensures that wave propagation to infinity does not take place at the interface or at the upper surface. In order to examine the existence of trapped modes, multipole expansion method, along with the properties of an infinite system of linear equations, is used. A number of observations are made on the trapped modes with regard to different submergence depths and depths of all the layers. For the frequencies below a cut-off value, there exist two modes (except for the rigid lid problem) for which trapped wave exists. For low density ratios, the motion of the first mode is concentrated about the upper surface while for the second mode, the motion is concentrated about the interface. As the density ratio increases, the motion for the first mode is transferred from the upper surface to the interface, and the upper surface elevation becomes very small. The dispersion relation is also analyzed for various water depths and for different submergence depths of the cylinder placed in either of the layers. In all these problems mentioned above, trapped mode frequencies are computed below a cut-off value. We have excluded the presence of surface tension at the free surface and interfaces. Its exclusion is justified by pre- 1

17 senting some numerical results in another problem. For the case when the effect of surface tension is included, we observe that out of the two modes of the dispersion curves, the higher mode gets more affected with the variation of the surface tension parameters. Variation of the trapped mode against density ratio does not get affected by the presence of surface tension either at the free surface or the interface. Therefore, we make the observation that in this type of problems, the inclusion of surface tension in the formulation does not lead to any significant difference. Though in this problem the upper layer is covered by a free surface, similar observation is expected when the free surface be replaced by a rigid lid or an ice-cover and hence it is justifiable to ignore surface tension altogether. The existence of trapped modes show that, in general, a radiation condition for the waves at infinity is insufficient for the uniqueness of the scattering problem. The solutions are expected to render a quantitative guidance to various types of water wave problems in two-layer and three-layer fluids. It is to be noted that the existence of trapped modes throughout the present work is based on numerical evidence only, i.e., the values of those frequencies are located numerically for which the truncated determinant vanishes. However, we feel that similar proofs for two-layer and three-layer fluids, as was done for a single-layer fluid by Ursell (1951), may be possible to be derived. This work was carried out with research scholar Ms. Sunanda Saha. 2 17

18 Dynamic Models for Infectious Diseases M. Naresh Kumar NRSC (ISRO), Hyderabad Abstract Role of vaccination and treatment Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In the present talk models that are of practical importance aimed at quick containment of diseases are discussed. The interplay of treatment and vaccination efforts on the spread of infection in presence of time delays is presented. Moreover, soft computing approaches for estimating the reproduction rate and a statistical method for building mathematical models from data forms an interesting part of this talk. 18

19 Finite Pointset Method - Some Important Issues S. Sundar IIT Madras, Chennai , India Abstract Finite Pointset Method, popularly known as FPM and a meshfree method, has been developed by Joerg Kuhnert and his team at Fraunhofer ITWM, Germany. This method is proven to be successful in many direct industrial applications, especially, for the problems involving moving boundaries, free surface flows etc. In this talk I will be focusing on the following important issues which are pondering in my mind: 1. Is it really a meshfree approach? 2. Is speed up at the simulation level is realizable (Hierarchical Partitioning, GPU FPM...)? 3. Is it a Lagrangian framework method? 19

20 Pricing, Hedging, and Risk: A Tutorial Vijaysekhar Chellaboina Mahindra-Ecole-Centrale, Hyderabad, , India Abstract Fair pricing of financial products, hedging of portfolios, and risk mitigation are three fundmental problems in mathematical and computational finance. In this seminar, we will present a breif introduction to each of these three problems by formulating appropriate stochastic optimal control problems. First part of the seminar will focus on the classical Black and Scholes framework for pricing and heding of financial derivatives followed by an introduction to risk measures and their computation. The talk will conclude with a unified stochastic optimization based framework for pricing, hedging, and risk mitigation. 20

21 Ray, Radon, Fourier Transforms and Inverse Problem in Image Reconstruction Nandakumaran, A. K. Department of Mathematics Indian Institute of Science Bangalore India. Abstract In this talk, we introduce Ray and Radon transforms in the context of Tomogrpahic reconstruction. We will see how Fourier transform is used in inverting the Radon Transform. Tomography is a cross sectional imaging of an object or tissue from the mathematical modelling and measured experimental data. The study of tomography involves mathematical modelling, analysis, development of numerical algorithms and its implementation and experimental validation. These problems lead to a class of inverse problems where the mathematical analysis and computations are rather complicated. Here, we plan to present a general introduction to tomography beginning with X-ray tomography and if time permits, move on to other tomographies like diffuse correlation tomography (DCT), ultrasound modulated optical tomography (UMOT). Most of the talk will be addressed to cater the general audience both from engineering and science. In our tour of tomography, you may get to see the importance of analysis like Radon transform, Fourier transform, various PDEs. This talk to be delivered at the National Conference on Latest Advances in Computational and Applied Mathematics (LACAM-2016) during December 15-17, 2016 at Mahindra Ecole Centrale (MEC) Institute, Hyderabad, India. 1 21

22 Far field boundary conditions and their approximation A. S. Vasudeva Murthy TIFR-Centre for Applicable MAthematics, Yelahanka, Bangalore Abstract Many PDE s are often formulated in unbounded domains. However for computing the solutions numerically we need to truncate it to a bounded domain. This introduces artificial boundaries and consequently artificial boundary conditions (ABC). The choice of ABC can be tricky and can lead to wrong solutions. We give a brief survey for ABC with some simple examples. 22

23 Modeling the activity of the entire primate brain: A meso-scale dynamical perspective Sitabhra Sinha The Institute of Mathematical Sciences, Chennai , India Abstract Nonlinear dynamics of interactions between clusters of neurons via complex networks lie at the base of all brain activity. How such communication between brain regions gives rise to the rich behavioral repertoire of the organism has been a long-standing question. In this talk, we will explore this question by looking at the simulations of collective dynamics of a detailed network of cortical areas in the Macaque brain recently compiled from the CoCoMac database, as well as, a model of global coupled brain regions used as a benchamrk. To understand the large-scale dynamics of the brain, we simulate it at the mesoscopic level with each node representing a local region of cortex, comprising between neurons. The dynamical behavior of each such region has been described using a phenomenological model consisting of a pool of excitatory neurons coupled to a pool of inhibitory neurons, which exhibits oscillations over a large range of parameter values. Coupling these regions according to the Macaque cortical network produces activation patterns strikingly similar to those observed in recordings from the brain. Our results help to connect recent experimental findings of the olfactory system and suggest that a part of the complicated activity patterns seen in the brain may be explained even without a full knowledge of its wiring diagram. 23

24 Optimal Paths using Differential Evolution for Missile pursuing Target Arya Kumar Bhattacharya, Pranay Thangeda and Rajeswary Gopal Mahindra Ecole Centrale, Hyderabad, India Abstract The problem of charting an optimal trajectory for an aircraft-launched missile pursuing an enemy target, from instants of launch to strike, with the objective of minimizing time of travel and satisfying multiple constraints, is resolved here using Differential Evolution an Evolutionary Optimization technique. The problem is handled by treating the nearroot-cause variables the normal and lateral accelerations as the design variables of the trajectory at discrete intervals spanning the complete time of travel. The other parameters of state of the trajectory, the effects, are extracted using the 3-DOF equations to relate the design variables to these state parameters through numerical solution. A novel cost function is generated which fuses the requirements of minimizing time and distance of travel using the supplement of the cost-to-go - the cost-as-yet approach. The combination of the Differential Evolution approach with this cost function yields missile trajectories that are best so far with respect to the stated objectives. 24

25 Conference on Latest Advances in Computational and Applied Mathematics(LACAM) Dec 2016, Mahindra cole Centrale (MEC), Hyderabad ABSTRACTS Finite Element Study of Mixed Convection Process in a Concentration Stratied Fluid Saturated Porous Enclosure S. V. S. S. N. V. G. Krishna Murthy 1 Department of Applied Mathematics, Defence Institute of Advanced Technology, Pune , India Vinay Kumar Department of Applied Mathematics, Defence Institute of Advanced Technology Deemed University, Pune , India B. V. Rathish Kumar Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur , India ABSTRACT Mixed convection flow, caused by combined process of natural convection and forced convection with the effects of thermal or species diffusion in a fluid saturated porous medium, has attracted the attention of several researchers due to its numerous applications. Some of these applications include, dispersion of chemical contaminants through water saturated soil, migration of moisture through air contained in brous insulation, in grain storage units, and in several other geothermal and engineering applications. In the present work, we numerically analyze double diffusive mixed convection flow in a two dimensional square porous enclosure under the influence of suction and injection on top and bottom walls respectively. i.e Free convection is induced by isothermal heated left vertical wall and the forced convection is imposed by the injection at the bottom wall and a suction at the top wall. The coupled non-linear partial differential equations governing the Darcy flow model / Forchheimer extended Darcy flow model has been used on mixed convection process. Full partial differential equations governing the flow, temperature and concentration transport, are solved using the finite element method. Detailed numerical computations are carried out for a wide range of governing parameters such as Rayleigh Number (Ra), suction / injection velocity (a), suction /injection width (D/H), as fraction of the length of the square enclosure and the results are analyzed by tracing the iso-concentration and streamlines of the domain both in absence / presence of inertial forces and stratification conditions REFERENCES [1] D.B. Ingham, I. Pop, Transport Phenomena in Porous Media, Pergamon, Oxford [2] K. Vafai, Handbook of Porous Media, Marcel Dekker, New York, [3] I. Pop, D.B. Ingham, Convective Heat tranfer: Mathematical and Computational Modeling of Viscous Fluid and Porous Media, Oxford: Pergamon, [4] A. Bejan, A. D. Krauss, Heat Transfer Hand book, Wiley, New York [5] D.B. Ingham, A. Bejan, A. Mamut, I. Pop, Emerging Technologies and Techniques in Porous Media, Kluwer, Dordrecht, [6] D.A. Nield, A. Bejan, Convection in Porous Media, 3 rd edition, Springer, New York, [7] B.V.R. Kumar, P. Singh, V.J. Bansod, Effect of thermal stratification on double diffusive natural convection in a vertical porous enclosure, Numerical Heat Transfer: Applications, 41, , [8] B.V. Rathish Kumar, Shalini, Natural convection in a thermally stratified wavy vertical porous enclosure, Numerical Heat Transfer: Part A, 43, , [9] B. V. Rathish Kumar, S. V. S. S. N. V. G. Krishna Murthy, Vivek Sangwan, Mohit Nigam, Peeyush Chandra, Non-Darcy Mixed Convection in a Fluid Saturated Square Porous Enclosure Under suction Effect Part-I, Journal of Porous Media, 13(6) (2010) [10] Shohel Mahmud and Ioan Pop, Mixed Convection in Square Vented Enclosure Filled with a Porous Medium, International Journal of Heat and Mass Transfer, 49, , Deemed University, Dept. of Defence R & D, Ministry of Defence, Govt. of India, Pune Phone: , Fax: , sgkmurthy@gmail.com, skmurthy@diat.ac.in, 1 25

26 Finite element methods for PDEs with moving boundaries Sashikumaar Ganesan Department of Computational and Data Sciences, Indian Institute of Science, Bangalore, India Abstract Fluid flows with moving boundaries are encountered in many applications such as spray cooling, spray coating, ink-jet printing, fuel injecting, fluid-structure interactions, aerodynamics, ship hydrodynamics, etc. The fluid flow and/or scalar quantities (temperature, concentration, etc) in these applications are described by parabolic PDEs (Navier-Stokes equations, energy equation, etc) in a time-dependent domain. Apart from other challenges associate with the numerical solution of these nonlinear PDEs, presence of the moving boundaries make the computations more challenging. In this talk, a finite element scheme based on arbitrary Lagrangian- Eulerian (ALE) approach will be presented for PDEs in time-dependent domain. After a brief discussion on the numerical challenges, the stability estimates for the continuous and discrete forms of the model will be provided. In addition, algorithms and implementations will be discussed. Finally, an array of numerical results for impinging droplets, rising bubble, flows with surfactants on free surface, flow over oscillating aerofoil, etc, will be presented. 26

27 Anewsmoothnessindicatorforthird-orderWENO scheme G. Naga Raju Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur , India Abstract The weighted essentially non-oscillatory scheme (WENO) is one of the promising methodologies to obtain an approximate solution for solving the hyperbolic conservation laws. A new global smoothness indicator is designed for the third-order WENO scheme, by which the scheme achieves the third order of accuracy in the presence of critical points. Numerical results for the conservation laws in one and two dimensions are presented to verify the robustness and accuracy of the scheme. 1 27

28 A variational multiscale scheme for incompressible Navier-Stokes equations in an arbitrary Lagrangian Eulerian setup Birupaksha Pal a and Sashikumaar Ganesan b Computational Mathematics Group, CDS, Indian Institute of Science, Bangalore , India. a birupaksha@gmail.com, b sashi@cds.iisc.in Turbulent flows are highly unsteady flows which displays a very chaotic nature. Here the velocity flow field is superimposed by random velocity fluctuations. LES, large eddy simulation, which resolves the larger scales of the flow while modeling the effect of the smaller unresolved scales on the larger ones by some turbulence model; with the scale separation handled by some filter function is a popular approach for numerical simulation of turbulent flows. Variational Multiscale method (VMS) [1,2,3] is a significant new development on the classical LES approach, where it does away with the commutation errors arising out of filtering. It also allows to separate of the entire range of scales into two or three groups. Thus a different numerical treatment for any of these scale groups is enabled. In addition when deforming domains are considered the computational complexity of the problem increases furthermore. In this talk an (ALE) arbitrary Lagrangian-Eulerian, based VMS scheme for computations of incompressible Navier-Stokes equations in time-dependent domains will be presented. The numerical scheme, based on [4] is a three-scale VMS with a projection based scale separation, where the large scales are represented by an additional tensor valued space. The resolved large and small scales are computed in a coupled way with the effects of unresolved scales confined only to the resolved small scales. The popular Smagorinsky eddy viscosity model is used to model the effects of unresolved scales. An elastic mesh update technique is used in the ALE approach. Moreover, a computationally efficient scheme is obtained by the choice of orthogonal finite element basis function for the resolved large scales. For numerical validation of the scheme, study on simulations of flow over a plunging aerofoil and an oscillating beam and will be presented. References [1] V. John and S. Kaya: A finite element variational method for the Navier-Stokes equations, SIAM. J. Sci. Comput, 26, (2005) [2] T. J. R. Hughes, L. Mazzei, K. E. Jansen: Large eddy simulation and the variational multiscale methods, Comp. Visu. Sci, 3, (2000) [3] V. Gravemeier, W. A. Wall, E. Ramm: Large eddy simulation of turbulent incompressible flows by a three-level finite element method, Int. J. Numer. Meth. Fluids, 48, (2005), [4] B. Pal, S. Ganesan: Projection based variational multiscale method for incompressible Navier Stokes equations in time-dependent domains, Int. J. Numer. Meth. Fluids, DOI: /fld

29 Polynomial Pressure Projection Stabilized (PPPS) FEM with an Application to Nanofluid Heat Transfer Victor M. Job, Sreehara Rao Gunakala Abstract We present a numerical study on unsteady MHD natural convection nanofluid flow within a wavy trapezoidal enclosure. The governing equations of the problem were solved using the Polynomial Pressure Projection Stabilized (PPPS) finite element method proposed by Bochev et al. (2004). The PPPS finite element method is a powerful tool for solving problems in the field of Computational Fluid Dynamics, since it allows for the use of efficient equal-order approximations of the velocity and pressure of the fluid under consideration. We briefly review this method and discuss its application to the aforementioned numerical study on convective nanofluid flow. The influence of a few important non-dimensional parameters, such as the nanoparticle solid fraction and Hartmann number, on the nanofluid flow and heat transfer is also presented. 29

30 Double-diffusive Hadley-Prats flow in a horizontal porous layer with a concentration based internal heat source Anjanna Matta Department of Mathematics, Faculty of science and Technology, IFHE University, Dontanapalli, Hyderabad, Telangana, India Abstract Double-diffusive Hadley-Prats flow with a concentration based heat source is investigated through linear and nonlinear stability analyses. The resultant eigenvalue problems for both theories are solved numerically using Shooting and fourth order Runga-Kutta methods, with the critical thermal Rayleigh number being evaluated with respect to various flow governing parameters such as the magnitudes of the heat source and mass flow. It is observed, in the linear case, that an increase in the horizontal thermal Rayleigh number is stabilising for both positive and negative values of the solutal Rayleigh number. In nonlinear case, a destabilizing effect is identified at higher mass flow rates. An increase in both the heat source and mass flow results in destabilisation. Key words: Double diffusive convection, porous medium, heat source, mass flow, Energy stability analysis. address: anjireddyiith@ifheindia.org (Anjanna Matta). 30

31 A high order numerical scheme for solving nonlinear singular boundary value problems Kiran Kumar Thula Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur , India. Abstract In this talk, I will present a high order accurate numerical scheme for solving a class of nonlinear singular two-point boundary value problem arising in various physical models in engineering and applied science. The method is based on a quartic B-spline collocation. I will discuss in detail the derivation of the method. Further, the error analysis and convergence of the method will be discussed. The efficiency and accuracy of the method are illustrated with six numerical examples, four of which have physical significance, including thermal explosion, non-linear heat conduction model of human head, stress distribution on a rotationally symmetric shallow membrane cap, reaction diffusion process inside a porous catalyst which is needed in the design of catalyst reactors. Numerical results show the present method is of fourth order. Comparison with other existing numerical techniques reveals that the proposed method has higher accuracy and efficiency. 1 31

32 Multi-time step domain decomposition method Manoj K. Yadav School of Natural Sciences, Mahindra École Centale, Hyderabad, Abstract Evolution of time dependent physical quantities, such as current, heat etc., in composite materials are modelled by initial boundary value problems for parabolic PDEs. These physical quantities follow differnent evolution patterns in different parts of the composite material depending on the material properties, size of constituent material subdomains, coupling scheme, etc. Therefore, the stability and accuracy requirements of a numerical integration scheme may necessitate domain dependent time discretization of the problem. Parabolic problems are usually solved by discretizing spatially using finite elemets and then integrating over time using discrete solvers. We propose an asynchronous multi-domain time integration scheme for solving initial boundary value problems of parabolic PDEs. For efficient parallel computing of large problems, we present the dual decomposition method with local Lagrange multipliers to ensure the continuity of the primary unknowns at the interface between subdomains. We also propose a multi-time step coupling method which enables us to use domain dependent Rothe method on different parts of a computational domain and thus provide an efficient and robust approach to solving large scale composite material problems more accurately. 1 32

33 Phase-ordering kinetics in martensitic triple-well model Landau free energies N. Shankaraiah, 1,2 Awadhesh Kumar Dubey, 1 Sanjay Puri, 1 and S. R. Shenoy 2 1 School of Physical Sciences, Jawaharlal Nehru University, New Delhi ,India. 2 TIFR Centre for Interdisciplinary Sciences, TIFR-Hyderabad , India. Abstract We present phase-ordering underdamped strain dynamics of 1-D Bales- Gooding triple-well model Landau free energy [1] in 2- and 3- spatial dimensions for square-rectangle and tetragonal-orthorhombic martensitic transitions [3] without power-law anisotropic interactions. After quenching a dilutely seeded austenite below a first-order transition, we find dynamical scaling in strain-strain correlation functions with a coarsening length L(t) t α and Porod s tail in structure factor for sharp interfaces [2, 4]. The exponent α behavior is understood by inserting the dynamical scaling ansatz into correlation function dynamics whose solutions g(t) 1/t α have exponent values matching with simulations [4]. Acknowledgements: NS would like to thank UGC-India for Dr.D.S. Kothari post-doctoral fellowship. References [1] G.S. Bales and R.J, Gooding, Phys. Rev. Lett. 67, 3412 (1991). [2] G. Porod, Small-Angle X-ray scattering, Academic Press, New York (1982); Sanjay Puri, Phase transitions, 77, 407 (2004). [3] S.R. Shenoy, T. Lookman and A. Saxena, Phys. Rev. B 82, (2010). [4] N. Shankaraiah, Awadhesh Kumar Dubey, Sanjay Puri and S.R. Shenoy, (Phys. Rev. B (2016) (In Press)). 1 33

34 Liquid Crystals confined to restricted geometries: A Monte Carlo Study Jayasri D School of Natural Sciences, Mahindra Ecole Centrale, Bahadurpally, Hyderabad Non-Boltzmann Monte Carlo methods have the distinct advantage of being able to generate the free energy landscape of the systems in great detail. This advantage is exploited to study the liquid crystal systems confined to restricted geometries like spherical, cylindrical and more recently toroidal droplets. Bulk order behaviour of nematic liquid crystals is studied to observe the effect of temperature vis-à-vis surface induced anchoring in such confined geometries [1]. Very recently liquid crystals confined to toroidal droplets with one or more handles are stabilized experimentally [2] giving rise to interesting director configurations in nematic phase. The focus of the present work is to investigate the effect of temperaure and surface induced anchoring on the bulk ordering of liquid crystal molecules in such restricted geometries, particularly near the nematic-isotropic (NI) phase transition using both Metropolis algorithm and non-boltzmann simulation techniques. The mapping between the complex director configurations present in the physical system and their statistical counterparts in the artificial ensembles generated via Wang-Landau based method are discussed. References: 1. D. Jayasri, et. al., Liquid crystal films on curved surfaces, Physica A, 390, (2011); G. S. Preeti, et. al., Monte Carlo study of radial and axial ordering in cylindrical films of liquid crystal, J. Comp. Mat. Sci., 44, 1, (2008). 2. E. Pairam, et. al., Stable nematic droplets with handles, Proc. Nat. Acad. Sci., 110, 23, (2013). 34

35 On the Convergence Rate of a Robin-Type Non-Overlapping Domain Decomposition Procedure for Second Order Parabolic Problems Debasish Pradhan Department of Applied Mathematics, Defence Institute of Advanced Technology, Girinagar, Pune , India. This article deals with the analysis of an iterative non overlapping domain decomposition (DD) method for parabolic problems, using Robin-type boundary condition on the inter-subdomain boundaries, which can be solved in parallel with local communications. In order to derive the corresponding discrete problem, we apply a non-conforming Galerkin method using the lowest order Crouzeix-Raviart elements. The convergence of the iterative scheme is obtained by proving that the spectral radius of the matrix associated with the fixed point iterations is less than 1. For t = O(h 2 ), we derive the upper bound of the rate of convergence which is of order 1 - O(h 1/2 H 1/2 ), where h is the finite element mesh parameter, H is the maximum diameter of the subdomains and t is the time step. The numerical experiments confirm the theoretical results established in this paper. keywords. parabolic problem, non-overlapping domain decomposition, Robin-type boundary condition, iterative procedure, non-conforming finite elements, Crouzeix-Raviart elements, spectral radius, rate of convergence. REFERENCES [1] D. Pradhan, B. Shalini, N. Nataraj and A. K. Pani, A Robin-Type Non-Overlapping Domain Decomposition Procedure for Second Order Elliptic Problems, Adv. Comput. Math., 34, pp (2011). [2] M. J. Gander, Optimized Schwarz methods, SIAM J. Numer. Anal. 44, pp (2006). [3] L. Qin and X. Xu, On a parallel Robin-type non-overlapping domain decomposition method, SIAM J. Numer. Anal. 44, pp (2006). [4] L. Qin and X. Xu, Optimized Schwarz methods with Robin transmission conditions for parabolic problems, SIAM J. Sci. Comput. 31, pp (2008). 35

36 FINITE ELEMENT METHOD FOR KELLER-SEGEL CHEMOTAXIS SYSTEM Arumugam Gurusamy Computational Biology Division DRDO-BU Center for Life Sciences Bharathiar University Campus, Coimbatore , India Abstract. In this work, we consider a finite element method for nonlinear parabolic - parabolic system of partial differential equations which describe the chemotactic features, called a Keller-Segel system with additional cross-diffusion term in the second equation. First we present a semi-implicit scheme for weak formulation of our prob lem and then we define fixed point formulation for the corresponding scheme. Next we prove the existence of approximate solutions by using Schauder s fixed point theorem. Further we establish a priori error estimate for the approximate solutions in H 1 norm. Finally, we present the numerical simulation. 1 36

37 UNIFORMLY CONVERGENT FINITE DIFFERENCE SCHEME FOR SINGULARLY PERTURBED SYSTEM OF CONVECTION-DIFFUSION TYPE DELAY DIFFERENTIAL EQUATIONS V. SUBBURAYAN 1 AND N. RAMANUJAM 2 Abstract. In this paper an uniformly convergent numerical method based on the finite difference scheme on Shishkin mesh is suggested to solve singularly perturbed boundary value problems for system of second order ordinary delay differential equation of convectiondiffusion type. An error estimate is derived and is found to be almost first order. Numerical results are provided to illustrate the theoretical results. Key words:weakly coupled system; Convection-diffusion equation; Delay differential equation; Shishkin mesh MSC2000 Subject Classification: 34K10, 34K26, 34K28 1 Department of Mathematics, SRM University, Kattankulathur, Kancheepuram , Tamilnadu, India. suburayan123@gmail.com 2 Department of Mathematics, Bharathidasan University, Tiruchirappalli , Tamilnadu, India. matram2k3@gmail.com. 1 37

38 Fourth Order Nonlinear Diffusion Filters for Image Denoising Mahipal Jetta Abstract In this talk a class of second order diffusion filters will be considered in removing the additive noise from an image. We show through simulations that this class removes noise but produces stair-case artifacts in the filtered image. A remedy for this problem will be suggested by considering a fourth order partial differential equation. Further we extend this idea to remove speckle noise present in an image. 1 38

39 Numerical solution of heat and mass transfer in fluidized beds using DG methods V Dhanya Varma 1, Suresh Kumar Nadupuri 1, and Chamakuri Nagaiah 2 1 National Institute of Technology, Calicut, Kerala 2 Mahindra École Centrale, Hyderabad, Telangana Abstract The aim of this work is to find efficient and reliable numerical solutions of concentration and temperature distribution in gas-solid-fluidized beds with spray injection. The model equations are strongly coupled and nonlinear partial differential equations with Dirichlet and Neumann boundary conditions. Solutions to these equations are approximated using the Discontinuous Galerkin methods for the spatial discretization and linearly implicit Runge-Kutta methods for temporal discretization. In this talk we present the numerical solution of concentrations distributions inside the fluidized beds. A study has been conducted to see the behaviour of process parameters for heat and mass transfer in fluidized beds. 1 39

40 SOLUTIONS TO FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN A BANACH SPACE Madhukant Sharma a, Shruti Dubey b a Mahindra École Centrale, Hyderabad b Indian Institute of Technology, Madras madhukant.sharma@mechyd.ac.in Abstract. This work is consecrated to investigate the existence of solutions to nonautonomous fractional functional differential equations in a general Banach space along with a nonlocal condition. The main results are proved by using fixed point techniques, classical semigroup theory and tools of fractional calculus. As an example, a nonlocal retarded elliptic evolution equation of fractional order has been given for demonstration. 1 40

41 TITLE: AN ORDER LEVEL INVENTORY MODEL UNDER L2-SYSTEM WITH QUADRATIC DEMAND WITH k-release RULE T.Santi sree1,dr.m.madhavilata2 and Dr.KondaReddy3 TGT,Finance and Accounts,University of Hyderabad Department of Maths,G.Narayanamma Institute of Technology & Science,Hyderabad,India Department of Maths,Konerilakshmaih University,Green Fields,Vaddeshwaram,Guntur Abstract: This paper deals with a single period inventory model for a deteriorating items having two levels of storage. Here the demand is assumed to be quadratic demand. The replenishment rate is infinite and the model is constructed with shortages which are fully backlogged.the solution of the model is illustrated with the help of a numerical example. Keywords:Two levels of storage,quadratic Demand,Shipments. 41

42 Constrained Rational Quartic Fractal Interpolation Surface Abstract In this paper, constrain problem for both α-fractal rational quartic spline and rational quartic fractal interpolation surface is discussed. First α-fractal rational quartic spline is constructed which contains one family of shape parameters. Conditions on scaling factors and shape parameters are derived so that α-fractal rational quartic spline lies above the given straight line whenever univariate interpolation data lies above the straight line. Then to interpolate bivariate data which lies on rectangular grid, fractal interpolation surface is constructed with the help of blending functions and α-fractal rational quartic splines. Conditions on scaling factors and shape parameters are derived so that fractal interpolation surface lies above the plane if surface data lies above the plane. 1 42

43 Impulse Response of the Viscous Burger s Equation with a Magneto-Rheological Viscosity Prasad Pokkunuri Institute of Infrastructure, Technology, Research, and Management (IITRAM) Maninagar (East), Ahmedabad Gujarat. INDIA Prasad.Pokkunuri@iitram.ac.in 23 rd November, 2016 Defence and automotive applications such as firearms, shock-absorbers and aircraft landing gear, to name a few, are subject to high impact and shock loading. Stringent requirements are placed on the systems response to these kind of loads. Field responsive fluids, which are a class of smart materials, are commonly used to absorb the impact energy and keep the resulting displacements and/or velocities within acceptable limits. By applying a magnetic or electric field, the fluids stress response can be controlled and used in a closedloop system. This work studies the behaviour of one type of fluid, viz. magneto rheological fluids, for use in defence applications. Magneto rheological fluids exhibit a change in rheological properties elasticity, plasticity, or viscosity with the application of a magnetic fluid. The well-known Burger s equation is used to represent fluid behaviour, without the additional complexities due to geometry, pressure, body forces, and other source terms. The Bingham power law and Kelvin-Voigt visco-elastic models are used to relate viscosity to fluid velocity. A finite-difference formulation is used to discretize the governing equation. First-order upwind, second-order central, and backward Euler schemes are used for advection, diffusion, and time derivative terms respectively. The response to an impulsive initial condition is studied, with no-outflow, no-inflow boundary conditions confining the disturbance within the problem domain. 43

44 RBF based grid free local scheme with an optimal shape parameter Satyanarayana Chirala Mahindra Ecole Centrale, Hyderabad, India Abstract The RBF based grid-free local numerical schemes (Sanyasiraju, 2007, 2008) are becoming popular particularly for solving fluid flow and heat transfer problems, due to their better conditioning, flexibility in handling the non-linearities and the independence of the space dimension. Franke (1982) has shown that Multi-Quadric (MQ), provides better results, when compared with the other radial functions like Gaussian and Splines. While the infinitely smooth RBFs like MQ, φ(r) = 1 + (εr) 2, where r = x x j 2, x, x j R d, ε is the (scaling) shape parameter, is used in the computations, the shape parameter plays a significant role in obtaining accurate and stable solutions. The main objective of this talk is to discuss the development of local algorithm to optimize the shape parameter for the RBF based grid-free local schemes (Sanyasiraju, 2007, 2008), such that, it provides the optimal scaling parameter for the infinitely smooth interpolant. 44

45 Seventh-order WENO scheme with the L 1 norm type smoothness indicators Samala Rathan Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur , India rathan.maths@gmail.com Abstract The construction and implementation of a seventh order weighted essentially non-oscillatory scheme to solve the hyperbolic conservation laws is analyzed. It is known that the smoothness indicators constructed based on L 1 norm approach may lead to provide a loss of regularity to the solution. To overcome this difficulty, smoothness indicators measured in L 1 norm are constructed based on developing an approximation method to derivatives with high order of accuracy. Higher order interpolation polynomial is used where each derivative is approximated to the fourth order of accuracy with respect to the evaluation point, as the scheme is of seventh order. Introduced a global smoothness indicator in order to satisfy the sufficient condition to get the required order of accuracy. Numerical solutions to the scalar test problems, one and twodimensional Euler system of equations are reported. 1 45

46 Formation of a stable ring of bubbles in a Couette device with Taylor vortices Jai Prakash School of Natural Sciences, Mahindra Ecole Centrale, Hyderabad , India Equal size air bubbles that are entrapped at the center streamline of a Taylor vortex of the secondary flow in a Couette device, thereby defying buoyancy, slowly form a stable ordered string with equal separation distances between all neighbors. This phenomenon repeats itself regardless of the number of bubbles in the flow. Hence, doublets will assume opposite positions, triplets will form a triangle, four bubbles will arrange in a square and so on. It is shown that the driving force to this dynamics is inertia effect. We present a model based on the dynamics of two bubbles positioned on the same streamline in a simple shear flow. The slow viscous flow is evaluated via the use of conformal mapping. This solution yields no force between the bubbles. The first order inertia correction is obtained via the use of the reciprocal theorem for creeping flow. It is shown that the inertia effect results in a force that changes the distance between the bubbles. When the initial position is not too close, the force pushes the bubbles apart from each other. In a rotating Couette device it is expected that the separation will increase until it is balanced by a similar counter force. 46