High resolution entropy stable scheme for shallow water equations
|
|
- Rhoda Hall
- 5 years ago
- Views:
Transcription
1 Internatonal Symposum on Computers & Informatcs (ISCI 05) Hgh resoluton entropy stable scheme for shallow water equatons Xaohan Cheng,a, Yufeng Ne,b, Department of Appled Mathematcs, Northwestern Polytechncal Unversty, X an 7007, Shaanx, Chna a chengxh68@63.com, b yfne@nwpu.edu.cn Abstract: A hgh resoluton entropy stable scheme s proposed for solvng shallow water equatons n ths paper. The scheme contans two parts: entropy conservatve flux and numercal dffuson operator. To acheve hgh resoluton, a lmter s employed to guarantee the numercal dffuson term beng added around the dscontnutes automatcally. Numercal experments are presented to demonstrate the proposed scheme s capacty. Keywords: entropy stable scheme, lmter, shallow water equatons, hgh resoluton Introducton Shallow water equatons, also known as the Sant-Venant system, are wdely used to model flows n rvers, lakes and near-shore oceans. In one dmensonal case the equatons can be wrtten as a system of balance laws U + f( U) = s( xu, ), wth U = [ h, hu] T beng the conservatve vector, T f = [ hu, hu + gh ] beng the flux vector, and s = [0, ghb ] T x beng the source term. Here, bx ( ) denotes the bottom topography, hxt (,) s the water t x () 05. The authors - Publshed by Atlants Press 078
2 heght above the bottom and uxt (,) s the depth-averaged water velocty. The constant g s the gravty acceleraton. In Eq. (), only the geometrcal source term s consdered. Other effects, such as wnd forces and frcton on the surface, are neglected. The most strkng feature of balance laws, as well as conservaton laws, s that solutons wth dscontnutes may appear n a fnte tme even for suffcent smooth ntal data []. Thus, solutons are n general sought n the weak sense. Due to the non-unqueness of weak solutons, an addtonal crteron, termed entropy condton, must be mposed to select the physcal soluton of our nterest. Numercal schemes whch respect a dscrete verson of the entropy dsspaton statement were called entropy stable schemes. Entropy stable scheme was frst presented by Tadmor [] and has attracted much attenton n recent years [3,4,5]. Most of them were based on entropy conservatve flux and sutable numercal dffuson operator. Entropy conservatve flux preserves the entropy exactly and behaves well n smooth regons. However, spurous oscllaton wll be produced around the dscontnutes, such as shocks. Thus, some dsspatve mechansm should be contaned to acheve entropy stablty. Compared wth the popular used Weghted Essentally Non-Oscllatory (WENO), Dscontnuous Galerkn (DG) methods [6,7], entropy stable schemes satsfy the system s addtonal condton,.e. entropy nequalty, and can avod some unphyscal phenomena. These methods are promsng when solvng realstc engneerng problems. In ths paper, a hgh resoluton entropy stable method s developed to solve shallow water equatons. The scheme conssts of a second order entropy conservatve flux and a Roe-type numercal dsspaton term. Unlke the approach n [8], numercal dsspaton term s actvated on the whole the whole doman and lowers the accuracy n smooth areas. Although a constructon of second order accurate s performed to avod ths, the resultng scheme cannot be entropy stable. Here, a lmter, whch sgnals the smooth degree of solutons, s employed to make the numercal dsspaton work around the dscontnutes automatcally. By ths way, the obtaned scheme stll guarantees entropy stablty. 079
3 When handng the source term, the well balance property s also taken nto account. Fnally, numercal examples are presented to verfy how well the scheme performs n practce. Numercal method For smplcty, unform grds of sze sem-dscrete fnte volume scheme s gven by x are consdered. Then, a standard Here, U s the cell average on I x / x+ / d U = ( F + / F / ) s. dt x () = [, ], F + / s the numercal flux consstent wth the flux f and s s a dscretzed source term. Tme ntegraton s carred out wth a second order strong stablty preservng (SSP) Runge-Kutta method [9]: gven a soluton n U at tme step t n, the soluton at the next tme level n U + s advanced by * n n n U = U + t LU ( ), n+ n * n * U = ( U + U + t LU ( ), ) (3) where L s the rght-hand sde of (). Shallow water system possesses an entropy functon E( U ) = ( hu + gh + ghb) and the entropy varables are defned E u by V= = [ gh ( + b), u] U functons are gven by T. Then, the correspondng entropy flux = + and 3 Q( U ) hu gh u 080
4 J ( x, U ) ghbu, as = respectvely. Defne the entropy potental T ψ = V f Q = guh. Accordng to the lemma n [8], a numercal flux F + s entropy conservatve f EC / V F g b h u T EC + / + / = ψ + + / + /, + / + / wth the notaton: a = a a + +, + / + / (4) a = ( a + a ). Then, EC analogous to the case wth flat bottom topography, F + / s determned by h+ /u+ / EC F + / =. g h + / + h + /( u + / ) To acheve the well balanced property, the source term s approxmated by 0 s = g. ( h+ / b + h / b + / / ) x Entropy conservatve flux preserves the total entropy and performs well n smooth regons. But t wll produce spurous oscllatons n the vcnty of dscontnutes. Ths problem s handled by usng a sutable numercal operator. Consder the followng numercal flux, F = F R F Λ R V ES EC T + / + / + / + / + / + / + / (5) wth, 08
5 R + / + / =, g u + / gh+ / u+ / + gh+ / ( + / + / + / + / ) Λ = dag u gh, u + gh, Φ = dag( φ, φ ). + / + / + / The parameter φ + / s computed by the Combned Superbee lmter[0]. We want to stress here that the above defned numercal flux s entropy stable. The ntroduced Φ possesses a property of beng close to at shocks and vanshng away from shocks so that the numercal dffuson works around dscontnutes automatcally. Numercal experments In all smulatons below, the gravtatonal constant s fxed to be g = and Neumann boundary condtons are mposed. The reference solutons are computed from a well balanced second order central upwnd scheme from [] on a mesh of 000 ponts. Frst, small perturbaton of a steady state soluton s consdered. The bottom contans a hump, 0.5(cos(0 π ( x 0.5)) + ), x 0.5 < 0. bx ( ) = 0, otherwse. The ntal data s set to be xt, = 0 ( h+ b) = + ε and u, = 0 = 0. The perturbaton constant ε equals to 0.0 for 0. < x < 0.. Ths example s smulated on a mesh of 00 grds and the water surface level h+ bat tme t = 0.7 s presented n Fg.. It s seen that the scheme resolves the wave accurately wthout numercal oscllatons. xt 08
6 Fg.. Small perturbaton of a steady state soluton. (a) Intal water surface level h+ b(sold lne) and bottom topography (dotted lne); (b) Water surface level h+ bat t = 0.7 (square: numercal soluton; sold lne: reference soluton) Fg.. A statonary shock n the transcrtcal case. (a) Intal water surface level h+ b(sold lne) and bottom topography (dotted lne); (b) Water surface level h+ bat t =.8 (square: numercal soluton; sold lne: reference soluton) 083
7 Next, a transcrtcal flow s smulated. The bottom topography s the same as the prevous example. The ntal water surface level s set to be and the ntal water velocty s taken to be 0.3. In ths example, a steady-state appears on the surface. The computaton s performed on a mesh of 00 grds up to tme t =.8 and Fg. dsplays the water surface level. Clearly, the shock s fully captured. Conclusons In ths paper, a hgh resoluton entropy stable method has been developed for smulatng shallow water flows. Its prncpal advantage, and a major dfference from other exstng methods, s that t acheves entropy stablty. The scheme s accuracy s mproved by usng a lmter. Numercal smulatons demonstrate the proposed scheme s effcent and hgh resoluton. Acknowledgements Ths research was fnancally supported by the Natonal Natural Scence Foundaton of Chna (7043, 476) and the Doctorate Foundaton of Northwestern Polytechncal Unversty (CX046). References []. RJ LeVeque, Fnte volume methods for hyperbolc problems. Vol : Cambrdge unversty press. []. E Tadmor. Math. Comp., 987, 49(79):9-03. [3]. E Tadmor. Acta Numer., 003, ():45-5. [4]. US Fjordholm, S Mshra, and E Tadmor. SIAM J. Numer. Anal., 0, 50(): [5]. A Hltebrand and S Mshra. Numer. Math., 04, 6():03-5. [6]. C-W Shu. SIAM Rev., 009, 5():8-6. [7]. B Cockburn and C-W Shu. J. Sc. Comput., 00, 6(3):73-6. [8]. US Fjordholm, S Mshra, and E Tadmor. J. Comput. Phys., 0, 084
8 30(4): [9]. S Gottleb, DI Ketcheson, and C-W Shu. J. Sc. Comput., 009, 38(3):5-89. [0]. PK Sweby. SIAM J. Numer. Anal., 984, (5): []. A Kurganov and D Levy. ESAIM: Math. Modell. Numer. Anal., 00, 36(3):
Appendix B. The Finite Difference Scheme
140 APPENDIXES Appendx B. The Fnte Dfference Scheme In ths appendx we present numercal technques whch are used to approxmate solutons of system 3.1 3.3. A comprehensve treatment of theoretcal and mplementaton
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationLecture 12: Discrete Laplacian
Lecture 12: Dscrete Laplacan Scrbe: Tanye Lu Our goal s to come up wth a dscrete verson of Laplacan operator for trangulated surfaces, so that we can use t n practce to solve related problems We are mostly
More informationNON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS
IJRRAS 8 (3 September 011 www.arpapress.com/volumes/vol8issue3/ijrras_8_3_08.pdf NON-CENTRAL 7-POINT FORMULA IN THE METHOD OF LINES FOR PARABOLIC AND BURGERS' EQUATIONS H.O. Bakodah Dept. of Mathematc
More informationCHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE
CHAPTER 5 NUMERICAL EVALUATION OF DYNAMIC RESPONSE Analytcal soluton s usually not possble when exctaton vares arbtrarly wth tme or f the system s nonlnear. Such problems can be solved by numercal tmesteppng
More informationLab session: numerical simulations of sponateous polarization
Lab sesson: numercal smulatons of sponateous polarzaton Emerc Boun & Vncent Calvez CNRS, ENS Lyon, France CIMPA, Hammamet, March 2012 Spontaneous cell polarzaton: the 1D case The Hawkns-Voturez model for
More informationChapter 5. Solution of System of Linear Equations. Module No. 6. Solution of Inconsistent and Ill Conditioned Systems
Numercal Analyss by Dr. Anta Pal Assstant Professor Department of Mathematcs Natonal Insttute of Technology Durgapur Durgapur-713209 emal: anta.bue@gmal.com 1 . Chapter 5 Soluton of System of Lnear Equatons
More informationMMA and GCMMA two methods for nonlinear optimization
MMA and GCMMA two methods for nonlnear optmzaton Krster Svanberg Optmzaton and Systems Theory, KTH, Stockholm, Sweden. krlle@math.kth.se Ths note descrbes the algorthms used n the author s 2007 mplementatons
More informationConvexity preserving interpolation by splines of arbitrary degree
Computer Scence Journal of Moldova, vol.18, no.1(52), 2010 Convexty preservng nterpolaton by splnes of arbtrary degree Igor Verlan Abstract In the present paper an algorthm of C 2 nterpolaton of dscrete
More informationA Hybrid Variational Iteration Method for Blasius Equation
Avalable at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 10, Issue 1 (June 2015), pp. 223-229 Applcatons and Appled Mathematcs: An Internatonal Journal (AAM) A Hybrd Varatonal Iteraton Method
More information1-Dimensional Advection-Diffusion Finite Difference Model Due to a Flow under Propagating Solitary Wave
014 4th Internatonal Conference on Future nvronment and nergy IPCB vol.61 (014) (014) IACSIT Press, Sngapore I: 10.776/IPCB. 014. V61. 6 1-mensonal Advecton-ffuson Fnte fference Model ue to a Flow under
More informationThe Finite Element Method
The Fnte Element Method GENERAL INTRODUCTION Read: Chapters 1 and 2 CONTENTS Engneerng and analyss Smulaton of a physcal process Examples mathematcal model development Approxmate solutons and methods of
More informationMATH 5630: Discrete Time-Space Model Hung Phan, UMass Lowell March 1, 2018
MATH 5630: Dscrete Tme-Space Model Hung Phan, UMass Lowell March, 08 Newton s Law of Coolng Consder the coolng of a well strred coffee so that the temperature does not depend on space Newton s law of collng
More informationPower law and dimension of the maximum value for belief distribution with the max Deng entropy
Power law and dmenson of the maxmum value for belef dstrbuton wth the max Deng entropy Bngy Kang a, a College of Informaton Engneerng, Northwest A&F Unversty, Yanglng, Shaanx, 712100, Chna. Abstract Deng
More information1. Introduction. The present work is devoted to the numerical approximations of weak solutions of the Euler equations: (1.1)
STABILITY OF THE MUSCL SCHEMES FOR THE EULER EQUATIONS CHRISTOPHE BERTHON Abstract. The second-order Van-Leer MUSCL schemes are actually one of the most popular hgh order scheme for flud dynamc computatons.
More informationpage 2 2 dscretzaton mantans ths stablty under a sutable restrcton on the tme step. SSP tme dscretzaton methods were frst developed by Shu n [20] and
page 1 A Survey of Strong Stablty Preservng Hgh Order Tme Dscretzatons Ch-Wang Shu Λ 1 Introducton Numercal soluton for ordnary dfferental equatons (ODEs) s an establshed research area. There are many
More informationDETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM
Ganj, Z. Z., et al.: Determnaton of Temperature Dstrbuton for S111 DETERMINATION OF TEMPERATURE DISTRIBUTION FOR ANNULAR FINS WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY BY HPM by Davood Domr GANJI
More informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationFTCS Solution to the Heat Equation
FTCS Soluton to the Heat Equaton ME 448/548 Notes Gerald Recktenwald Portland State Unversty Department of Mechancal Engneerng gerry@pdx.edu ME 448/548: FTCS Soluton to the Heat Equaton Overvew 1. Use
More informationThe Two-scale Finite Element Errors Analysis for One Class of Thermoelastic Problem in Periodic Composites
7 Asa-Pacfc Engneerng Technology Conference (APETC 7) ISBN: 978--6595-443- The Two-scale Fnte Element Errors Analyss for One Class of Thermoelastc Problem n Perodc Compostes Xaoun Deng Mngxang Deng ABSTRACT
More informationModule 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
More informationApplication of B-Spline to Numerical Solution of a System of Singularly Perturbed Problems
Mathematca Aeterna, Vol. 1, 011, no. 06, 405 415 Applcaton of B-Splne to Numercal Soluton of a System of Sngularly Perturbed Problems Yogesh Gupta Department of Mathematcs Unted College of Engneerng &
More informationInductance Calculation for Conductors of Arbitrary Shape
CRYO/02/028 Aprl 5, 2002 Inductance Calculaton for Conductors of Arbtrary Shape L. Bottura Dstrbuton: Internal Summary In ths note we descrbe a method for the numercal calculaton of nductances among conductors
More informationA hybrid kinetic WENO scheme for compressible flow simulations
Tenth Internatonal onference on omputatonal Flud Dynamcs (IFD10), Barcelona, Span, July 9-13, 2018 IFD10-389 A hybrd knetc WENO scheme for compressble flow smulatons Hongwe Lu *, hangpng Yu, Xnlang L *orrespondng
More informationc 2006 Society for Industrial and Applied Mathematics
SIAM J. SCI. COMPUT. Vol. 8, No. 5, pp. 197 1956 c 6 Socety for Industral and Appled Mathematcs BEHAVIOR OF FINITE VOLUME SCHEMES FOR HYPERBOLIC CONSERVATION LAWS ON ADAPTIVE REDISTRIBUTED SPATIAL GRIDS
More informationNew Method for Solving Poisson Equation. on Irregular Domains
Appled Mathematcal Scences Vol. 6 01 no. 8 369 380 New Method for Solvng Posson Equaton on Irregular Domans J. Izadan and N. Karamooz Department of Mathematcs Facult of Scences Mashhad BranchIslamc Azad
More informationAdditional Codes using Finite Difference Method. 1 HJB Equation for Consumption-Saving Problem Without Uncertainty
Addtonal Codes usng Fnte Dfference Method Benamn Moll 1 HJB Equaton for Consumpton-Savng Problem Wthout Uncertanty Before consderng the case wth stochastc ncome n http://www.prnceton.edu/~moll/ HACTproect/HACT_Numercal_Appendx.pdf,
More informationLecture 5.8 Flux Vector Splitting
Lecture 5.8 Flux Vector Splttng 1 Flux Vector Splttng The vector E n (5.7.) can be rewrtten as E = AU (5.8.1) (wth A as gven n (5.7.4) or (5.7.6) ) whenever, the equaton of state s of the separable form
More information(Online First)A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate
Internatonal Journal of Mathematcs and Systems Scence (018) Volume 1 do:10.494/jmss.v1.815 (Onlne Frst)A Lattce Boltzmann Scheme for Dffuson Equaton n Sphercal Coordnate Debabrata Datta 1 *, T K Pal 1
More informationTensor Smooth Length for SPH Modelling of High Speed Impact
Tensor Smooth Length for SPH Modellng of Hgh Speed Impact Roman Cherepanov and Alexander Gerasmov Insttute of Appled mathematcs and mechancs, Tomsk State Unversty 634050, Lenna av. 36, Tomsk, Russa RCherepanov82@gmal.com,Ger@npmm.tsu.ru
More informationCOEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN
Int. J. Chem. Sc.: (4), 04, 645654 ISSN 097768X www.sadgurupublcatons.com COEFFICIENT DIAGRAM: A NOVEL TOOL IN POLYNOMIAL CONTROLLER DESIGN R. GOVINDARASU a, R. PARTHIBAN a and P. K. BHABA b* a Department
More informationNote 10. Modeling and Simulation of Dynamic Systems
Lecture Notes of ME 475: Introducton to Mechatroncs Note 0 Modelng and Smulaton of Dynamc Systems Department of Mechancal Engneerng, Unversty Of Saskatchewan, 57 Campus Drve, Saskatoon, SK S7N 5A9, Canada
More informationLectures - Week 4 Matrix norms, Conditioning, Vector Spaces, Linear Independence, Spanning sets and Basis, Null space and Range of a Matrix
Lectures - Week 4 Matrx norms, Condtonng, Vector Spaces, Lnear Independence, Spannng sets and Bass, Null space and Range of a Matrx Matrx Norms Now we turn to assocatng a number to each matrx. We could
More informationA MODIFIED METHOD FOR SOLVING SYSTEM OF NONLINEAR EQUATIONS
Journal of Mathematcs and Statstcs 9 (1): 4-8, 1 ISSN 1549-644 1 Scence Publcatons do:1.844/jmssp.1.4.8 Publshed Onlne 9 (1) 1 (http://www.thescpub.com/jmss.toc) A MODIFIED METHOD FOR SOLVING SYSTEM OF
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationLecture 13 APPROXIMATION OF SECOMD ORDER DERIVATIVES
COMPUTATIONAL FLUID DYNAMICS: FDM: Appromaton of Second Order Dervatves Lecture APPROXIMATION OF SECOMD ORDER DERIVATIVES. APPROXIMATION OF SECOND ORDER DERIVATIVES Second order dervatves appear n dffusve
More informationThe Study of Teaching-learning-based Optimization Algorithm
Advanced Scence and Technology Letters Vol. (AST 06), pp.05- http://dx.do.org/0.57/astl.06. The Study of Teachng-learnng-based Optmzaton Algorthm u Sun, Yan fu, Lele Kong, Haolang Q,, Helongang Insttute
More informationUniqueness of Weak Solutions to the 3D Ginzburg- Landau Model for Superconductivity
Int. Journal of Math. Analyss, Vol. 6, 212, no. 22, 195-114 Unqueness of Weak Solutons to the 3D Gnzburg- Landau Model for Superconductvty Jshan Fan Department of Appled Mathematcs Nanjng Forestry Unversty
More informationJournal of Fluid Science and Technology
Journal of Flud Scence and Technology Numercal Smulaton of Incompressble Flows around a Fsh Model at Low Reynolds Number Usng Seamless Vrtual Boundary Method * Hdetosh NISHIDA ** and Kyohe TAJIRI ** **Department
More informationStudy on Active Micro-vibration Isolation System with Linear Motor Actuator. Gong-yu PAN, Wen-yan GU and Dong LI
2017 2nd Internatonal Conference on Electrcal and Electroncs: echnques and Applcatons (EEA 2017) ISBN: 978-1-60595-416-5 Study on Actve Mcro-vbraton Isolaton System wth Lnear Motor Actuator Gong-yu PAN,
More informationBoundary Layer to a System of Viscous Hyperbolic Conservation Laws
Acta Mathematcae Applcatae Snca, Englsh Seres Vol. 24, No. 3 (28) 523 528 DOI: 1.17/s1255-8-861-6 www.applmath.com.cn Acta Mathema ca Applcatae Snca, Englsh Seres The Edtoral Offce of AMAS & Sprnger-Verlag
More informationPositivity-preserving time discretizations for production-destruction equations. with applications to non-equilibrium flows.
Postvty-preservng tme dscretzatons for producton-destructon equatons wth applcatons to non-equlbrum flows Juntao Huang and Ch-Wang Shu Abstract In ths paper, we construct a famly of modfed Patankar Runge-Kutta
More information2 Finite difference basics
Numersche Methoden 1, WS 11/12 B.J.P. Kaus 2 Fnte dfference bascs Consder the one- The bascs of the fnte dfference method are best understood wth an example. dmensonal transent heat conducton equaton T
More informationHongyi Miao, College of Science, Nanjing Forestry University, Nanjing ,China. (Received 20 June 2013, accepted 11 March 2014) I)ϕ (k)
ISSN 1749-3889 (prnt), 1749-3897 (onlne) Internatonal Journal of Nonlnear Scence Vol.17(2014) No.2,pp.188-192 Modfed Block Jacob-Davdson Method for Solvng Large Sparse Egenproblems Hongy Mao, College of
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationSIMULATION OF WAVE PROPAGATION IN AN HETEROGENEOUS ELASTIC ROD
SIMUATION OF WAVE POPAGATION IN AN HETEOGENEOUS EASTIC OD ogéro M Saldanha da Gama Unversdade do Estado do o de Janero ua Sào Francsco Xaver 54, sala 5 A 559-9, o de Janero, Brasl e-mal: rsgama@domancombr
More informationHigher Order Wall Boundary Conditions for Incompressible Flow Simulations
THE 5 TH ASIAN COMPUTAITIONAL FLUID DYNAMICS BUSAN KOREA OCTOBER 7-30 003 Hgher Order Wall Boundary Condtons for Incompressble Flow Smulatons Hdetosh Nshda. Department of Mechancal and System Engneerng
More informationA new Approach for Solving Linear Ordinary Differential Equations
, ISSN 974-57X (Onlne), ISSN 974-5718 (Prnt), Vol. ; Issue No. 1; Year 14, Copyrght 13-14 by CESER PUBLICATIONS A new Approach for Solvng Lnear Ordnary Dfferental Equatons Fawz Abdelwahd Department of
More informationENTROPY CONSERVATIVE SCHEMES AND ADAPTIVE MESH SELECTION FOR HYPERBOLIC CONSERVATION LAWS
Journal of Hyperbolc Dfferental Equatons Vol. 7, No. 3 () 383 44 c World Scentfc Publshng Company DOI:.4/S989677 ENTROPY CONSERVATIVE SCHEMES AND ADAPTIVE MESH SELECTION FOR HYPERBOLIC CONSERVATION LAWS
More informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
More informationOptimal Control of Temperature in Fluid Flow
Kawahara Lab. 5 March. 27 Optmal Control of Temperature n Flud Flow Dasuke YAMAZAKI Department of Cvl Engneerng, Chuo Unversty Kasuga -3-27, Bunkyou-ku, Tokyo 2-855, Japan E-mal : d33422@educ.kc.chuo-u.ac.jp
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationNumerical Simulation of One-Dimensional Wave Equation by Non-Polynomial Quintic Spline
IOSR Journal of Matematcs (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 14, Issue 6 Ver. I (Nov - Dec 018), PP 6-30 www.osrournals.org Numercal Smulaton of One-Dmensonal Wave Equaton by Non-Polynomal
More informationNumerical Solution of two dimensional coupled viscous Burgers Equation using the Modified Cubic B-Spline Differential Quadrature Method
umercal Soluton of two dmensonal coupled vscous Burgers Equaton usng the odfed Cubc B-Splne Dfferental Quadrature ethod H. S. Shukla 1, ohammad Tamsr 1*, Vneet K. Srvastava, Ja Kumar 3 1 Department of
More informationRobust MUSCL Schemes for Ten-Moment Gaussian Closure Equations with Source Terms
Robust MUSCL Schemes for Ten-Moment Gaussan Closure Equatons wth Source Terms Asha Meena, Harsh Kumar To cte ths verson: Asha Meena, Harsh Kumar. Robust MUSCL Schemes for Ten-Moment Gaussan Closure Equatons
More informationPositivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes
J Sc Comput 23 57:9 4 DOI.7/s95-3-9695-y Postvty-Preservng Well-Balanced Dscontnuous Galerkn Methods for the Shallow Water Equatons on Unstructured Trangular Meshes Yulong Xng Xangxong Zhang Receved: 9
More information6.3.4 Modified Euler s method of integration
6.3.4 Modfed Euler s method of ntegraton Before dscussng the applcaton of Euler s method for solvng the swng equatons, let us frst revew the basc Euler s method of numercal ntegraton. Let the general from
More informationModified Mass Matrices and Positivity Preservation for Hyperbolic and Parabolic PDEs
COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Commun. Numer. Meth. Engng 2000; 00:6 Prepared usng cnmauth.cls [Verson: 2000/03/22 v.0] Modfed Mass Matrces and Postvty Preservaton for Hyperbolc and
More informationTurbulent Flow. Turbulent Flow
http://www.youtube.com/watch?v=xoll2kedog&feature=related http://br.youtube.com/watch?v=7kkftgx2any http://br.youtube.com/watch?v=vqhxihpvcvu 1. Caothc fluctuatons wth a wde range of frequences and
More informationUpwind schemes for the wave equation in second-order form
Upwnd schemes for the wave equaton n second-order form Jeffrey W. Banks a,,, Wllam D. Henshaw a, a Center for Appled Scentfc Computng, Lawrence Lvermore Natonal Laboratory, Lvermore, CA 9455, USA Abstract
More informationChp 3: Scalar Advection and Linear Hyperbolic Systems. By Prof. Dinshaw S. Balsara
Chp 3: Scalar Advecton and Lnear Hyperbolc Systems By Prof. Dnshaw S. Balsara 3.) Introducton We have seen the need for consstency and stablty n FDAs of PDEs. However, for the advecton equaton, whch s
More informationNUMERICAL DIFFERENTIATION
NUMERICAL DIFFERENTIATION 1 Introducton Dfferentaton s a method to compute the rate at whch a dependent output y changes wth respect to the change n the ndependent nput x. Ths rate of change s called the
More informationInexact Newton Methods for Inverse Eigenvalue Problems
Inexact Newton Methods for Inverse Egenvalue Problems Zheng-jan Ba Abstract In ths paper, we survey some of the latest development n usng nexact Newton-lke methods for solvng nverse egenvalue problems.
More informationParameter Estimation for Dynamic System using Unscented Kalman filter
Parameter Estmaton for Dynamc System usng Unscented Kalman flter Jhoon Seung 1,a, Amr Atya F. 2,b, Alexander G.Parlos 3,c, and Klto Chong 1,4,d* 1 Dvson of Electroncs Engneerng, Chonbuk Natonal Unversty,
More informationLecture 21: Numerical methods for pricing American type derivatives
Lecture 21: Numercal methods for prcng Amercan type dervatves Xaoguang Wang STAT 598W Aprl 10th, 2014 (STAT 598W) Lecture 21 1 / 26 Outlne 1 Fnte Dfference Method Explct Method Penalty Method (STAT 598W)
More informationOperating conditions of a mine fan under conditions of variable resistance
Paper No. 11 ISMS 216 Operatng condtons of a mne fan under condtons of varable resstance Zhang Ynghua a, Chen L a, b, Huang Zhan a, *, Gao Yukun a a State Key Laboratory of Hgh-Effcent Mnng and Safety
More information829. An adaptive method for inertia force identification in cantilever under moving mass
89. An adaptve method for nerta force dentfcaton n cantlever under movng mass Qang Chen 1, Mnzhuo Wang, Hao Yan 3, Haonan Ye 4, Guola Yang 5 1,, 3, 4 Department of Control and System Engneerng, Nanng Unversty,
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationSome modelling aspects for the Matlab implementation of MMA
Some modellng aspects for the Matlab mplementaton of MMA Krster Svanberg krlle@math.kth.se Optmzaton and Systems Theory Department of Mathematcs KTH, SE 10044 Stockholm September 2004 1. Consdered optmzaton
More informationCollege of Computer & Information Science Fall 2009 Northeastern University 20 October 2009
College of Computer & Informaton Scence Fall 2009 Northeastern Unversty 20 October 2009 CS7880: Algorthmc Power Tools Scrbe: Jan Wen and Laura Poplawsk Lecture Outlne: Prmal-dual schema Network Desgn:
More informationSolving Fractional Nonlinear Fredholm Integro-differential Equations via Hybrid of Rationalized Haar Functions
ISSN 746-7659 England UK Journal of Informaton and Computng Scence Vol. 9 No. 3 4 pp. 69-8 Solvng Fractonal Nonlnear Fredholm Integro-dfferental Equatons va Hybrd of Ratonalzed Haar Functons Yadollah Ordokhan
More informationNeuro-Adaptive Design - I:
Lecture 36 Neuro-Adaptve Desgn - I: A Robustfyng ool for Dynamc Inverson Desgn Dr. Radhakant Padh Asst. Professor Dept. of Aerospace Engneerng Indan Insttute of Scence - Bangalore Motvaton Perfect system
More informationReport on Image warping
Report on Image warpng Xuan Ne, Dec. 20, 2004 Ths document summarzed the algorthms of our mage warpng soluton for further study, and there s a detaled descrpton about the mplementaton of these algorthms.
More information6.3.7 Example with Runga Kutta 4 th order method
6.3.7 Example wth Runga Kutta 4 th order method Agan, as an example, 3 machne, 9 bus system shown n Fg. 6.4 s agan consdered. Intally, the dampng of the generators are neglected (.e. d = 0 for = 1, 2,
More informationMarkov Chain Monte Carlo Lecture 6
where (x 1,..., x N ) X N, N s called the populaton sze, f(x) f (x) for at least one {1, 2,..., N}, and those dfferent from f(x) are called the tral dstrbutons n terms of mportance samplng. Dfferent ways
More informationON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EQUATION
Advanced Mathematcal Models & Applcatons Vol.3, No.3, 2018, pp.215-222 ON A DETERMINATION OF THE INITIAL FUNCTIONS FROM THE OBSERVED VALUES OF THE BOUNDARY FUNCTIONS FOR THE SECOND-ORDER HYPERBOLIC EUATION
More informationInternational Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sc. Technol., 4() (03), pp. 5-30 Internatonal Journal of Pure and Appled Scences and Technology ISSN 9-607 Avalable onlne at www.jopaasat.n Research Paper Schrödnger State Space Matrx
More informationNumerical Simulation of Wave Propagation Using the Shallow Water Equations
umercal Smulaton of Wave Propagaton Usng the Shallow Water Equatons Junbo Par Harve udd College 6th Aprl 007 Abstract The shallow water equatons SWE were used to model water wave propagaton n one dmenson
More informationA Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods
Advances n Appled Mathematcs and Mechancs Adv. Appl. Math. Mech., Vol., No., pp. -9 DOI:.8/aamm..m June A Comparson of the Performance of Lmters for Runge-Kutta Dscontnuous Galerkn Methods Hongqang Zhu,
More informationThe lower and upper bounds on Perron root of nonnegative irreducible matrices
Journal of Computatonal Appled Mathematcs 217 (2008) 259 267 wwwelsevercom/locate/cam The lower upper bounds on Perron root of nonnegatve rreducble matrces Guang-Xn Huang a,, Feng Yn b,keguo a a College
More informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and non-conservatve forces Mechancal Energy Conservaton of Mechancal
More informationAn Interactive Optimisation Tool for Allocation Problems
An Interactve Optmsaton ool for Allocaton Problems Fredr Bonäs, Joam Westerlund and apo Westerlund Process Desgn Laboratory, Faculty of echnology, Åbo Aadem Unversty, uru 20500, Fnland hs paper presents
More informationHandout: Large Eddy Simulation I. Introduction to Subgrid-Scale (SGS) Models
Handout: Large Eddy mulaton I 058:68 Turbulent flows G. Constantnescu Introducton to ubgrd-cale (G) Models G tresses should depend on: Local large-scale feld or Past hstory of local flud (va PDE) Not all
More informationLecture 2: Numerical Methods for Differentiations and Integrations
Numercal Smulaton of Space Plasmas (I [AP-4036] Lecture 2 by Lng-Hsao Lyu March, 2018 Lecture 2: Numercal Methods for Dfferentatons and Integratons As we have dscussed n Lecture 1 that numercal smulaton
More informationCOMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
More informationCase Study of Markov Chains Ray-Knight Compactification
Internatonal Journal of Contemporary Mathematcal Scences Vol. 9, 24, no. 6, 753-76 HIKAI Ltd, www.m-har.com http://dx.do.org/.2988/cms.24.46 Case Study of Marov Chans ay-knght Compactfcaton HaXa Du and
More informationSuppose that there s a measured wndow of data fff k () ; :::; ff k g of a sze w, measured dscretely wth varable dscretzaton step. It s convenent to pl
RECURSIVE SPLINE INTERPOLATION METHOD FOR REAL TIME ENGINE CONTROL APPLICATIONS A. Stotsky Volvo Car Corporaton Engne Desgn and Development Dept. 97542, HA1N, SE- 405 31 Gothenburg Sweden. Emal: astotsky@volvocars.com
More informationA Parameter Free Generalized Moment Limiter for High-Order Methods on Unstructured Grids
Advances n Appled Mathematcs and Mechancs Adv. Appl. Math. Mech., Vol. 1, No. 4, pp. 451-480 DOI: 10.4208/aamm.09-m0913 August 2009 A Parameter Free Generalzed Moment Lmter for Hgh-Order Methods on Unstructured
More informationPART 8. Partial Differential Equations PDEs
he Islamc Unverst of Gaza Facult of Engneerng Cvl Engneerng Department Numercal Analss ECIV 3306 PAR 8 Partal Dfferental Equatons PDEs Chapter 9; Fnte Dfference: Ellptc Equatons Assocate Prof. Mazen Abualtaef
More informationA PROCEDURE FOR SIMULATING THE NONLINEAR CONDUCTION HEAT TRANSFER IN A BODY WITH TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY.
Proceedngs of the th Brazlan Congress of Thermal Scences and Engneerng -- ENCIT 006 Braz. Soc. of Mechancal Scences and Engneerng -- ABCM, Curtba, Brazl,- Dec. 5-8, 006 A PROCEDURE FOR SIMULATING THE NONLINEAR
More informationGeneral viscosity iterative method for a sequence of quasi-nonexpansive mappings
Avalable onlne at www.tjnsa.com J. Nonlnear Sc. Appl. 9 (2016), 5672 5682 Research Artcle General vscosty teratve method for a sequence of quas-nonexpansve mappngs Cuje Zhang, Ynan Wang College of Scence,
More informationA stable, robust and high order accurate numerical method for Eulerian simulation of spray and particle transport on unstructured meshes
Center for Turbulence Research Annual Research Brefs 01 05 A stable, robust and hgh order accurate numercal method for Euleran smulaton of spray and partcle transport on unstructured meshes By A. Larat,
More informationParametric fractional imputation for missing data analysis. Jae Kwang Kim Survey Working Group Seminar March 29, 2010
Parametrc fractonal mputaton for mssng data analyss Jae Kwang Km Survey Workng Group Semnar March 29, 2010 1 Outlne Introducton Proposed method Fractonal mputaton Approxmaton Varance estmaton Multple mputaton
More informationThe Analysis of Convection Experiment
Internatonal Conference on Appled Scence and Engneerng Innovaton (ASEI 5) The Analyss of Convecton Experment Zlong Zhang School of North Chna Electrc Power Unversty, Baodng 7, Chna 469567@qq.com Keywords:
More informationSTUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS
Blucher Mechancal Engneerng Proceedngs May 0, vol., num. www.proceedngs.blucher.com.br/evento/0wccm STUDY ON TWO PHASE FLOW IN MICRO CHANNEL BASED ON EXPERI- MENTS AND NUMERICAL EXAMINATIONS Takahko Kurahash,
More informationThe equation of motion of a dynamical system is given by a set of differential equations. That is (1)
Dynamcal Systems Many engneerng and natural systems are dynamcal systems. For example a pendulum s a dynamcal system. State l The state of the dynamcal system specfes t condtons. For a pendulum n the absence
More informationSemi-supervised Classification with Active Query Selection
Sem-supervsed Classfcaton wth Actve Query Selecton Jao Wang and Swe Luo School of Computer and Informaton Technology, Beng Jaotong Unversty, Beng 00044, Chna Wangjao088@63.com Abstract. Labeled samples
More informationCombined Wronskian solutions to the 2D Toda molecule equation
Combned Wronskan solutons to the 2D Toda molecule equaton Wen-Xu Ma Department of Mathematcs and Statstcs, Unversty of South Florda, Tampa, FL 33620-5700, USA Abstract By combnng two peces of b-drectonal
More informationECE 534: Elements of Information Theory. Solutions to Midterm Exam (Spring 2006)
ECE 534: Elements of Informaton Theory Solutons to Mdterm Eam (Sprng 6) Problem [ pts.] A dscrete memoryless source has an alphabet of three letters,, =,, 3, wth probabltes.4,.4, and., respectvely. (a)
More informationANSWERS. Problem 1. and the moment generating function (mgf) by. defined for any real t. Use this to show that E( U) var( U)
Econ 413 Exam 13 H ANSWERS Settet er nndelt 9 deloppgaver, A,B,C, som alle anbefales å telle lkt for å gøre det ltt lettere å stå. Svar er gtt . Unfortunately, there s a prntng error n the hnt of
More information