Available online at ScienceDirect. Procedia Engineering 126 (2015 )

Size: px
Start display at page:

Download "Available online at ScienceDirect. Procedia Engineering 126 (2015 )"

Transcription

1 Availabl onlin at ScincDirct Procdia Enginring 26 (25 ) t Intrnational Confrnc on Fluid Mcanics, ICFM7 Applications of ig ordr ybrid DG/FV scms for twodimnsional RAS simulations Ming Li a, *, Wi Liu b, Laiping Zang a,b, Xin H a,b a Cina Arodynamics Rsarc and Dvlopmnt Cntr, Mianyang Sicuan, 62, Cina b Stat Ky Laboratory of Arodynamics, Mianyang Sicuan, 62, Cina Abstract A class of ig ordr ybrid DG/FV scms ad bn dvlopd for consrvation laws basd on a ybrid rconstruction ida. In tis papr, t ybrid DG/FV scms ar tndd to solv 2D RAS quations on unstructurd/ybrid grids. T BR2 approac is mployd to discrtiz t viscous trms and t Spalart-Allmaras modl is adoptd in t RAS quations to simulat t turbulnc ffct. T costs of som DG and DG/FV scms ar analyzd. Turbulnt flows ovr a flat plat and ovr 3P3 airfoil ar simulatd to validat t prformanc of t ybrid DG/FV scms. T numrical tsts sow tat t tird ordr DG/FV(3) scm obtains similar rsults wit tos form DGM(3), and can rduc t CPU cost gratly. 25 T Autors. Publisd by by Elsvir Ltd. Ltd. Tis is an opn accss articl undr t CC BY-C-D licns (ttp://crativcommons.org/licnss/by-nc-nd/4./). Pr-rviw undr rsponsibility of T Cins Socity of Tortical and Applid Mcanics (CSTAM). Pr-rviw undr rsponsibility of T Cins Socity of Tortical and Applid Mcanics (CSTAM) Kywords: discontinuous Galrkin Mtod; DG/FV scm; ybrid scm; RAS; Spalart-Allmaras modl;. Introduction Wit t rapid dvlopmnt of Computational Fluid Dynamics (CFD) and computr scinc, muc progrss about unstructurd/ybrid ms gnration tcniqu and numrical mtods av bn acivd ovr t past svral dcads. Altoug scond ordr finit volum mtods av bcom t main coic of most commrcial CFD cods, and bn provn succssful for a wid varity of flow problms in nginring applications, many in t CFD community bliv tat t simulations of vort-dominatd flows, sparation flows, turbulnt flows call for ig-ordr mtods to captur t fin structur of t flow fild. In fact, tr av bn intnsiv rsarc fforts * Corrsponding autor. Tl.: addrss: mli@sina.com T Autors. Publisd by Elsvir Ltd. Tis is an opn accss articl undr t CC BY-C-D licns (ttp://crativcommons.org/licnss/by-nc-nd/4./). Pr-rviw undr rsponsibility of T Cins Socity of Tortical and Applid Mcanics (CSTAM) doi:.6/j.prong

2 Ming Li t al. / Procdia Enginring 26 ( 25 ) on ig-ordr mtods for numrical simulation on unstructurd grids in t last two dcads. An incomplt list of notabl ampls includs P P M mtods [], t k-act Finit Volum mtod [2], discontinuous Galrkin (DG) mtod [3], Spctral Volum (SV) [4] and Spctral Diffrnc (SD) [5] mtods, RDG (Rconstructd DG), EO/WEO mtods and ig-ordr rsidual distribution mtods. In our prvious work [6-], a concpt of static rconstruction and dynamic rconstruction was introducd for igr-ordr (tird-ordr and igr) numrical mtods. Basd on tis concpt, a class of ybrid DG/FV scms as bn dvlopd for consrvation laws using a ybrid rconstruction approac. In ts ybrid DG/FV scms, t lowr-ordr cofficints of t picwis polynomial ar computd locally in a cll by t traditional DG mtod (calld as dynamic rconstruction ), wil t igr-ordr cofficints ar obtaind by t static rconstruction, using t known lowr-ordr cofficints in t cll itslf and in its nigboring clls. T static rconstruction approac can b viwd as a gnralization of t k-act rconstruction oprator proposd for finit volum mtod in t work of Rf.[2]. Ts ybrid DG/FV scms av bn tndd to solv 2D Eulr/-S quations on triangular and Cartsian/triangular ybrid grids. Comparing wit t wll-known DG scms wit t sam ordr of accuracy, t igr fficincy for tis ybrid mtod is vrifid. In tis papr, t ybrid DG/FV scms ar tndd to solv 2D RAS quations on ybrid grid. T ida of BR2 is mployd to obtain t viscous flu and t SA modl is adoptd to simulat t turbulnc ffct. In ordr to sow t ig fficincy of t prsnt ybrid DG/FV scms, t computational costs ar analyzd and compard wit t corrsponding DG mtods. T numrical prformanc is validatd by som typical tst cass, including t turbulnt flows ovr a flat plat and ovr 3P3 airfoil. T numrical tsts sow tat t tird ordr DG/FV(3) scm obtains similar rsults wit t sam ordr DGM(3), and can obtain similar rsults using coarsr grid comparing wit t scond ordr FVM. Qualitativ analysis dmonstrat tat ty can rduc t CPU cost gratly (up to 5%) comparing wit t traditional DG mtod wit t sam ordr of accuracy. 2. Govrning quations and DG/FV ybrid scms 2.. Govrning quations T control quations can b prssd in consrvativ form as U F F () t c v wr U is t consrvativ variabl vctor, F c is t convctiv flu vctor and F v is t viscous flu vctor, s Rf.[4] for mor dtails. To simulat t turbulnc ffct, t Spalart-Allmaras on-quation modl is adoptd in t RAS quations. T turbulnt viscosity is prssd ast f v, wr is t dpndnt variabl. T quation to solv is 2 2 ( c c b2 ) ( u j ) c b S c f w w ( ) (2) t j d j j j j T cofficints in Eq. (2) can b obtaind from Rf.[], and in tis work t Eqs. () and (2) ar solvd by using a dcoupling approac DG/FV ybrid rconstruction T govrning quations in Eq. () can b discrtizd using DG/FV ybrid scms. W assum tat t domain is dividd into a collction of non-ovrlapping lmnts { }, wr is t -t lmnt, and tn w introduc t following spac V of solution vctor m V {( v) : v P ( ) } (3)

3 63 Ming Li t al. / Procdia Enginring 26 ( 25 ) wic consists of discontinuous vctor polynomial functions of dgr P DG, and wr m is t dimnsion of t PFV unknown vctor and P is t spac of all polynomials of dgr P DG. W dfin rconstruction spac V similarly, wr PFV is t ordr of t rconstruction polynomial functions. In lmnt, t unknown vctor U and rconstruction vctor W can b prssd as U c b ( ) l l l M M b l ( l ) lb l l l W c ( ) l U cl l ( ) (4) wr c and l c ar t cofficints of t polynomials, bl ( ) is takn as ortogonal polynomial in rfrnc lmnt, and l is local coordinat vctor of t rfrnc lmnt, is t dimnsion of t unknown vctor spac and M is t dgr of frdom of rconstruction vctor spac To formulat t DG/FV scm, w introduc t following wak formulation, wic is obtaind by multiplying Eq. () by a tst function b j, intgrating ovr an lmnt, tn prforming an intgration by parts: tat is to find P U V DG suc tat ( U ) bd H nb d ( F F ) b d H n b d j,2,... (5) t j c j c v j v j wr U and W ar rprsntd by picwis polynomial functions of dgrs P DG and P FV rspctivly, wic ar discontinuous btwn t lmnt intrfacs, and n t unit outward normal vctor to t boundary of. Wn calculating t rigt and sid of Eq. (5), t igr ordr rconstruction vctor W ratr tan picwis polynomial U is adoptd and W is obtaind by a rconstruction algoritm using U of lmnt and its nigbor lmnts, s Rfs.[6-] for dtails. Sinc b j is t ortogonal basis of polynomial function as dscribd abov, Eq. (5) is quivalnt to t following systm of quations dc j RHS ( F F ) b d H nb d H n b d j,2,... (6) c v j c j v j dt wr is t volum of t lmnt. Sinc t numrical solution U is discontinuous btwn lmnt intrfacs, t intrfac flus ar not uniquly dfind. In t prsnt work, t Ro s scm [2] and Bassi-Rbay II scm [3] ar usd for valuating t inviscid and viscous numrical flus, rspctivly. Tis scm is calld DG/FV ybrid scms of ordr PFV, or in sort notation DG/FV( PFV ) scm. In tis work w us PFV if not writtn plicitly, wic mans tat t rconstruction polynomial is on ordr igr tan t solution polynomial. By incrasing t dgr of t polynomials P FV, t corrsponding igr ordr DG/FV ybrid scms ar obtaind. T tim dirction discrtization and boundary conditions tc. ar not writtn r for t sak of simplicity. 3. Tsts and discussion In tis sction, t costs of svral DG and DG/FV scms ar analyzd qualitativly and svral typical tsts ar rprsntd to illustrat t prformanc of t proposd DG/FV scms on RAS quations. 3.. Costs analysis T rfrnc [4] as givn som costs of svral DG scms basd on an assumption about t computation cost of numrical flu. In tis work t costs of svral DG and DG/FV scms ar analyzd qualitativly in t similar way and ar prsntd in Tabl to sow t rason wy t DG/FV scms ar capr tan t sam

4 63 Ming Li t al. / Procdia Enginring 26 (25) ordr DG scms. Form Tabl w can s tat t cost of lmnt intgral plays a vital rol in DG scms and t DG/FV scm wit t sam ordr is capr mainly bcaus its lmnt intgral part is capr, and tis av bn provd by numrical tsts, s Rfs. [6-] for mor dtails. Tabl. Costs of svral DG and DG/FV scms. Scms Variabls in quadratur vrtics Flu in quadratur vrtics Elmnt Rconstructi on Total costs intgral Boundary intgral Compard to t sam ordr DGM DGM(2) 45 DG/FV(3) DGM(3) 49% DG/FV(4) % DGM(4) Flat plat T turbulnt flow ovr a flat plat wit frstram Mac numbr.2 and t Rynolds numbr.3 7 is computd. T siz of coars grid usd for DG/FV(3) scm is 6 4, and t grid siz of t first layr from t solid wall is 2-3 in dirction and 2-6 in y dirction. T siz of fin grid usd for 2nd ordr FVM scm is 7 6, and t first grid siz is -3 in dirction and -6 in y dirction. T obtaind u profil at t sam position is prsntd in Fig., and sows good agrmnt wit t tortical rsult givn by Wigardt. Also, t rsults of t 3rd ordr DG/FV(3) scm on coars grid agr wll wit tos of 2nd ordr FVM on fin grid. Fig.. vlocity u profil of turbulnt flat plat (a)fvm on fin grid; (b)dg/fv(3) on coars grid. p y Ep. DG/FV(3) DGM(3) -Cp Fig. 2. (a) prssur contours and stramlins; (b) Prssur cofficint..2

5 632 Ming Li t al. / Procdia Enginring 26 ( 25 ) P3 airfoil T stady flow ovr a 3P3 airfoil is considrd as t scond tst cas. T frstram Mac numbr is.2, t Rynolds numbrs is 9 6 and t angl of attack is 9. A ybrid grid wit 95 quadrilatrals and 733 triangls is usd, and tr ar 662 vrtics on t airfoil. Figur 2 (a) sows t prssur contours and stramlins of 3P3 airfoil wit t 3rd DG/FV(3) scm. T prssur cofficint is givn in Fig. 2 (b) and t rsult from DG/FV(3) agrs wll wit t DGM(3) rsults on t sam grid and t rfrnc rsults [3]. 4. Conclusions and futur work In tis work, a class of ig ordr DG/FV ybrid scms is applid to solv RAS quations on twodimnsional unstructurd/ybrid grids using t Spalart-Allmaras on-quation modl. T turbulnt flows ovr a flat plat and ovr 3P3 airfoil ar simulatd to validat prformanc of t ybrid DG/FV scms. T tsts sow tat t 3rd ordr ybrid DG/FV(3) scm can gt similar rsults wit DGM(3) and can obtains similar rsults wit t scond ordr FVM but using coarsr grid. T cost analysis sows tat t DG/FV ybrid scms ar capr tan t DG scms of t sam ordr, and plains wy ty ar. W ar currntly tnding t DG/FV ybrid scms to tr-dimnsional cass, and t rsults will b prsntd in a futur publication. Acknowldgmnts Tis work was supportd by ational atural Scinc Foundation of Cina (Grant 4229). Rfrncs [] M. Dumbsr, D.S. Balsara, E.F. Toro, t al. A unifid framwork for t construction of on-stp finit volum and discontinuous Galrkin scms on unstructurd mss, J. Comput. Pys., 227 (28) [2] C. Ollivir-Gooc, A. jat, K. Micalak, Obtaining and vrifying ig-ordr unstructurd finit volum solutions to t Eulr quations, AIAA Journal, 47 (29) [3] B. Cockburn, C.W. Su, T Rung-Kutta discontinuous Galrkin finit lmnt mtod for consrvation laws V: multidimnsional systms, J. Comput. Pys. 4 (998) [4] Y. Sun, Z.J. Wang, Y. Liu, Spctral (finit) volum mtod for consrvation laws on unstructurd grids VI: tnsion to viscous flow, J. Comput. Pys., 25 (26) [5] Y. Sun, Z.J. Wang, Y. Liu, Hig-Ordr Multi-Domain spctral diffrnc mtod for t avir-stoks quations on unstructurd adral grids, Commun. Comput. Pys.,2 (26) [6] L.P. Zang, W. Liu, L.X. H, t al. A class of ybrid DG/FV mtods for consrvation laws I: Basic formulation and on-dimnsional systms. J. Comput. Pys., 23 (22) 8-3. [7] L.P. Zang, W. Liu, L.X. H, t al. A class of ybrid DG/FV mtods for consrvation laws II: Two-dimnsional cass. J. Comput. Pys., 23 (22) 4-2. [8] L.P. Zang, W. Liu, L.X. H, t al. A class of ybrid DG/FV mtods for consrvation laws III: Two-Dimnsional Eulr Equations. Commun. Comput. Pys., 2 (22) [9] L.P. Zang, W. Liu, M. Li, t al. A class of DG/FV ybrid scms for consrvation law IV: 2D viscous flows and implicit algoritm, Computrs & Fluids, 97(24) -25. [] L.P. Zang, M. Li, W. Liu, t al. An implicit algoritm for ig-ordr DG/FV scms for comprssibl flows on 2D arbitrary grids, Commun. Comput. Pys., 7 (25) [] W. Ptrson, W.Z. David, Tr-dimnsional arodynamic computations on unstructurd grids using a wton-krylov approac, Computr & Fluids, 37 (28) 7-2. [2] P.L. Ro, Approimat Rimann solvrs, paramtr vctors, and diffrnc scms, J. Comput. Pys.,43 (98) [3] F. Bassi, S. Rbay, G. Mariottig, t al. A ig-ordr accurat discontinuous finit lmnt mtod for inviscid and viscous turbomacinry flows, in 2 nd Europan confrnc on turbomacinry fluid dynamics and trmodynamics, Blgium, pp. 99-8,997. [4] Y.Z. Sun, Z.J. Wang, Evaluation of discontinuous Galrkin and spctral volum mtods for scalar and systm consrvation laws on unstructurd grids, Int. J. umr. Mt. Fluids, 45 (24)

AS 5850 Finite Element Analysis

AS 5850 Finite Element Analysis AS 5850 Finit Elmnt Analysis Two-Dimnsional Linar Elasticity Instructor Prof. IIT Madras Equations of Plan Elasticity - 1 displacmnt fild strain- displacmnt rlations (infinitsimal strain) in matrix form

More information

Characteristics of Gliding Arc Discharge Plasma

Characteristics of Gliding Arc Discharge Plasma Caractristics of Gliding Arc Discarg Plasma Lin Li( ), Wu Bin(, Yang Ci(, Wu Cngkang ( Institut of Mcanics, Cins Acadmy of Scincs, Bijing 8, Cina E-mail: linli@imc.ac.cn Abstract A gliding arc discarg

More information

COMPUTATIONAL NUCLEAR THERMAL HYDRAULICS

COMPUTATIONAL NUCLEAR THERMAL HYDRAULICS COMPUTTIONL NUCLER THERML HYDRULICS Cho, Hyoung Kyu Dpartmnt of Nuclar Enginring Soul National Univrsity CHPTER4. THE FINITE VOLUME METHOD FOR DIFFUSION PROBLEMS 2 Tabl of Contnts Chaptr 1 Chaptr 2 Chaptr

More information

ME469A Numerical Methods for Fluid Mechanics

ME469A Numerical Methods for Fluid Mechanics ME469A Numrical Mthods for Fluid Mchanics Handout #5 Gianluca Iaccarino Finit Volum Mthods Last tim w introducd th FV mthod as a discrtization tchniqu applid to th intgral form of th govrning quations

More information

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA *

Dynamic Modelling of Hoisting Steel Wire Rope. Da-zhi CAO, Wen-zheng DU, Bao-zhu MA * 17 nd Intrnational Confrnc on Mchanical Control and Automation (ICMCA 17) ISBN: 978-1-6595-46-8 Dynamic Modlling of Hoisting Stl Wir Rop Da-zhi CAO, Wn-zhng DU, Bao-zhu MA * and Su-bing LIU Xi an High

More information

Homotopy perturbation technique

Homotopy perturbation technique Comput. Mthods Appl. Mch. Engrg. 178 (1999) 257±262 www.lsvir.com/locat/cma Homotopy prturbation tchniqu Ji-Huan H 1 Shanghai Univrsity, Shanghai Institut of Applid Mathmatics and Mchanics, Shanghai 272,

More information

Finite Element Model of a Ferroelectric

Finite Element Model of a Ferroelectric Excrpt from th Procdings of th COMSOL Confrnc 200 Paris Finit Elmnt Modl of a Frrolctric A. Lópz, A. D Andrés and P. Ramos * GRIFO. Dpartamnto d Elctrónica, Univrsidad d Alcalá. Alcalá d Hnars. Madrid,

More information

Effects of Couple Stress Lubricants on Pressure and Load Capacity of Infinitely Wide Exponentially Shaped Slider Bearing

Effects of Couple Stress Lubricants on Pressure and Load Capacity of Infinitely Wide Exponentially Shaped Slider Bearing Procdings of t World Congrss on Enginring and Computr Scinc 200 Vol II, Octobr 20-22, 200, San Francisco, USA Effcts of Coupl Strss Lubricants on Prssur and Load Capacity of Infinitly Wid Eponntially Sapd

More information

Analysis of potential flow around two-dimensional body by finite element method

Analysis of potential flow around two-dimensional body by finite element method Vol. 7(2), pp. 9-22, May, 2015 DOI: 10.5897/JMER2014.0342 rticl Numbr: 20E80053033 ISSN 2141 2383 Copyright 2015 uthor(s) rtain th copyright of this articl http://www.acadmicjournals.org/jmer Journal of

More information

y=h B 2h Z y=-h ISSN (Print) Dr. Anand Swrup Sharma

y=h B 2h Z y=-h ISSN (Print) Dr. Anand Swrup Sharma Scolars Journal of Enginring and Tcnology (SJET) Sc. J. Eng. Tc., 5; 3(A):4-54 Scolars Acadmic and Scintific ublisr (An Intrnational ublisr for Acadmic and Scintific Rsourcs) www.saspublisr.com ISSN 3-435X

More information

3-2-1 ANN Architecture

3-2-1 ANN Architecture ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.

More information

Finite element discretization of Laplace and Poisson equations

Finite element discretization of Laplace and Poisson equations Finit lmnt discrtization of Laplac and Poisson quations Yashwanth Tummala Tutor: Prof S.Mittal 1 Outlin Finit Elmnt Mthod for 1D Introduction to Poisson s and Laplac s Equations Finit Elmnt Mthod for 2D-Discrtization

More information

2008 AP Calculus BC Multiple Choice Exam

2008 AP Calculus BC Multiple Choice Exam 008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl

More information

A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME

A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME A NEW SIGNATURE PROTOCOL BASED ON RSA AND ELGAMAL SCHEME ABSTRACT J Ettanfoui and O Kadir Laboratory of Matmatics, Cryptograpy and Mcanics, Fstm, Univrsity Hassan II of Casablanca, Morocco In tis papr,

More information

EDGE-BASED DATA STRUCTURES FOR THE PARALLEL SOLUTION OF 3D STEADY INCOMPRESSIBLE FLUID FLOW WITH THE SUPG/PSPG FINITE ELEMENT FORMULATION.

EDGE-BASED DATA STRUCTURES FOR THE PARALLEL SOLUTION OF 3D STEADY INCOMPRESSIBLE FLUID FLOW WITH THE SUPG/PSPG FINITE ELEMENT FORMULATION. Procdings of t XXVI Ibrian Latin-Amrican Congrss on Computational Mtods in Enginring CILAMCE 2005 Brazilian Assoc. for Comp. Mcanics (ABMEC) & Latin Amrican Assoc. of Comp. Mtods in Enginring (AMC), Guarapari,

More information

Higher-Order Discrete Calculus Methods

Higher-Order Discrete Calculus Methods Highr-Ordr Discrt Calculus Mthods J. Blair Prot V. Subramanian Ralistic Practical, Cost-ctiv, Physically Accurat Paralll, Moving Msh, Complx Gomtry, Slid 1 Contxt Discrt Calculus Mthods Finit Dirnc Mimtic

More information

Construction of Mimetic Numerical Methods

Construction of Mimetic Numerical Methods Construction of Mimtic Numrical Mthods Blair Prot Thortical and Computational Fluid Dynamics Laboratory Dltars July 17, 013 Numrical Mthods Th Foundation on which CFD rsts. Rvolution Math: Accuracy Stability

More information

An Efficiency Substructure Method for Nonlinear SSI Analysis of Large-scale Concrete Structures in Time Domain on the ANSYS Platform

An Efficiency Substructure Method for Nonlinear SSI Analysis of Large-scale Concrete Structures in Time Domain on the ANSYS Platform An Efficincy Substructur Mthod for Nonlinar SSI Analysis of Larg-scal Concrt Structurs in Tim Domain on th ANSYS Platform J. B. Li, X. Q. Yin, G. Lin School of Civil and Hydraulic Enginring, Dalian Univrsity

More information

Difference -Analytical Method of The One-Dimensional Convection-Diffusion Equation

Difference -Analytical Method of The One-Dimensional Convection-Diffusion Equation Diffrnc -Analytical Mthod of Th On-Dimnsional Convction-Diffusion Equation Dalabav Umurdin Dpartmnt mathmatic modlling, Univrsity of orld Economy and Diplomacy, Uzbistan Abstract. An analytical diffrncing

More information

3 Finite Element Parametric Geometry

3 Finite Element Parametric Geometry 3 Finit Elmnt Paramtric Gomtry 3. Introduction Th intgral of a matrix is th matrix containing th intgral of ach and vry on of its original componnts. Practical finit lmnt analysis rquirs intgrating matrics,

More information

ruhr.pad An entropy stable spacetime discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations

ruhr.pad An entropy stable spacetime discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations Bild on Scrift: rur.pad UA Rur Zntrum für partill Diffrntialglicungn Bild mit Scrift: rur.pad UA Rur Zntrum für partill Diffrntialglicungn An ntropy stabl spactim discontinuous Galrkin mtod for t two-dimnsional

More information

Physics 43 HW #9 Chapter 40 Key

Physics 43 HW #9 Chapter 40 Key Pysics 43 HW #9 Captr 4 Ky Captr 4 1 Aftr many ours of dilignt rsarc, you obtain t following data on t potolctric ffct for a crtain matrial: Wavlngt of Ligt (nm) Stopping Potntial (V) 36 3 4 14 31 a) Plot

More information

Discontinuous Galerkin methods

Discontinuous Galerkin methods ZAMM Z. Angw. Mat. Mc. 83, No. 11, 731 754 2003 / DOI 10.1002/zamm.200310088 Discontinuous Galrkin mtods Plnary lctur prsntd at t 80t Annual GAMM Confrnc, Augsburg, 25 28 Marc 2002 Brnardo Cockburn Univrsity

More information

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient

Full Waveform Inversion Using an Energy-Based Objective Function with Efficient Calculation of the Gradient Full Wavform Invrsion Using an Enrgy-Basd Objctiv Function with Efficint Calculation of th Gradint Itm yp Confrnc Papr Authors Choi, Yun Sok; Alkhalifah, ariq Ali Citation Choi Y, Alkhalifah (217) Full

More information

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h

is an appropriate single phase forced convection heat transfer coefficient (e.g. Weisman), and h For t BWR oprating paramtrs givn blow, comput and plot: a) T clad surfac tmpratur assuming t Jns-Lotts Corrlation b) T clad surfac tmpratur assuming t Tom Corrlation c) T clad surfac tmpratur assuming

More information

A UNIFIED A POSTERIORI ERROR ESTIMATOR FOR FINITE VOLUME METHODS FOR THE STOKES EQUATIONS

A UNIFIED A POSTERIORI ERROR ESTIMATOR FOR FINITE VOLUME METHODS FOR THE STOKES EQUATIONS A UNIFIED A POSTERIORI ERROR ESTIMATOR FOR FINITE VOLUME METHODS FOR THE STOKES EQUATIONS JUNPING WANG, YANQIU WANG, AND XIU YE Abstract. In tis papr, t autors stablisd a unifid framwork for driving and

More information

843. Efficient modeling and simulations of Lamb wave propagation in thin plates by using a new spectral plate element

843. Efficient modeling and simulations of Lamb wave propagation in thin plates by using a new spectral plate element 843. Efficint modling and simulations of Lamb wav propagation in thin plats by using a nw spctral plat lmnt Chunling Xu, Xinwi Wang Stat Ky Laboratory of Mchanics and Control of Mchanical Structurs aning

More information

Journal of Computational and Applied Mathematics. An adaptive discontinuous finite volume method for elliptic problems

Journal of Computational and Applied Mathematics. An adaptive discontinuous finite volume method for elliptic problems Journal of Computational and Applid Matmatics 235 (2011) 5422 5431 Contnts lists availabl at ScincDirct Journal of Computational and Applid Matmatics journal ompag: www.lsvir.com/locat/cam An adaptiv discontinuous

More information

Finite Element Models for Steady Flows of Viscous Incompressible Fluids

Finite Element Models for Steady Flows of Viscous Incompressible Fluids Finit Elmnt Modls for Stad Flows of Viscous Incomprssibl Fluids Rad: Chaptr 10 JN Rdd CONTENTS Govrning Equations of Flows of Incomprssibl Fluids Mid (Vlocit-Prssur) Finit Elmnt Modl Pnalt Function Mthod

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

A Weakly Over-Penalized Non-Symmetric Interior Penalty Method

A Weakly Over-Penalized Non-Symmetric Interior Penalty Method Europan Socity of Computational Mthods in Scincs and Enginring (ESCMSE Journal of Numrical Analysis, Industrial and Applid Mathmatics (JNAIAM vol.?, no.?, 2007, pp.?-? ISSN 1790 8140 A Wakly Ovr-Pnalizd

More information

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME Introduction to Finit Elmnt Analysis Chaptr 5 Two-Dimnsional Formulation Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt

More information

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force

Dynamic response of a finite length euler-bernoulli beam on linear and nonlinear viscoelastic foundations to a concentrated moving force Journal of Mchanical Scinc and Tchnology 2 (1) (21) 1957~1961 www.springrlink.com/contnt/1738-9x DOI 1.17/s1226-1-7-x Dynamic rspons of a finit lngth ulr-brnoulli bam on linar and nonlinar viscolastic

More information

UNIFIED ERROR ANALYSIS

UNIFIED ERROR ANALYSIS UNIFIED ERROR ANALYSIS LONG CHEN CONTENTS 1. Lax Equivalnc Torm 1 2. Abstract Error Analysis 2 3. Application: Finit Diffrnc Mtods 4 4. Application: Finit Elmnt Mtods 4 5. Application: Conforming Discrtization

More information

Discontinuous Galerkin Approximations for Elliptic Problems

Discontinuous Galerkin Approximations for Elliptic Problems Discontinuous Galrkin Approximations for lliptic Problms F. Brzzi, 1,2 G. Manzini, 2 D. Marini, 1,2 P. Pitra, 2 A. Russo 2 1 Dipartimnto di Matmatica Univrsità di Pavia via Frrata 1 27100 Pavia, Italy

More information

A LOCALLY CONSERVATIVE LDG METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A LOCALLY CONSERVATIVE LDG METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS A LOCALLY CONSERVATIVE LDG METHOD FOR THE INCOMPRESSIBLE NAVIER-STOES EQUATIONS BERNARDO COCBURN, GUIDO ANSCHAT, AND DOMINI SCHÖTZAU Abstract. In this papr, a nw local discontinuous Galrkin mthod for th

More information

Analysis of Convection-Diffusion Problems at Various Peclet Numbers Using Finite Volume and Finite Difference Schemes Anand Shukla

Analysis of Convection-Diffusion Problems at Various Peclet Numbers Using Finite Volume and Finite Difference Schemes Anand Shukla Mathmatical Thory and Modling.iist.org ISSN 4-5804 (apr) ISSN 5-05 (Onlin) Vol., No.6, 01-Slctd from Intrnational Confrnc on Rcnt Trnds in Applid Scincs ith nginring Applications Analysis of Convction-iffusion

More information

Instantaneous Cutting Force Model in High-Speed Milling Process with Gyroscopic Effect

Instantaneous Cutting Force Model in High-Speed Milling Process with Gyroscopic Effect Advancd Matrials sarch Onlin: -8-6 ISS: 66-8985, Vols. 34-36, pp 389-39 doi:.48/www.scintific.nt/am.34-36.389 rans ch Publications, Switzrland Instantanous Cutting Forc Modl in High-Spd Milling Procss

More information

16. Electromagnetics and vector elements (draft, under construction)

16. Electromagnetics and vector elements (draft, under construction) 16. Elctromagntics (draft)... 1 16.1 Introduction... 1 16.2 Paramtric coordinats... 2 16.3 Edg Basd (Vctor) Finit Elmnts... 4 16.4 Whitny vctor lmnts... 5 16.5 Wak Form... 8 16.6 Vctor lmnt matrics...

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

More information

The Autonomous Underwater Vehicle (AUV) MAYA: General Description

The Autonomous Underwater Vehicle (AUV) MAYA: General Description Introduction h ocans and rivrs always hav bn and still ar an important sourc of rvnu and prosprity for mankind. Du to th grat importanc of ocans and rivrs, th scintific community maks us of Autonomous

More information

Introduction to Computational Fluid Dynamics: Governing Equations, Turbulence Modeling Introduction and Finite Volume Discretization Basics.

Introduction to Computational Fluid Dynamics: Governing Equations, Turbulence Modeling Introduction and Finite Volume Discretization Basics. Introduction to Computational Fluid Dynamics: Govrning Equations, Turbulnc Modling Introduction and Finit Volum Discrtization Basics. Jol Gurrro Fbruary 13, 2014 Contnts 1 Notation and Mathmatical rliminaris

More information

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis

Middle East Technical University Department of Mechanical Engineering ME 413 Introduction to Finite Element Analysis Middl East Tchnical Univrsity Dpartmnt of Mchanical Enginring ME 43 Introduction to Finit Elmnt Analysis Chaptr 3 Computr Implmntation of D FEM Ths nots ar prpard by Dr. Cünyt Srt http://www.m.mtu.du.tr/popl/cunyt

More information

FINITE ELEMENT ANALYSIS OF SLOSHING IN LIQUID-FILLED CONTAINERS

FINITE ELEMENT ANALYSIS OF SLOSHING IN LIQUID-FILLED CONTAINERS FINIE ELEMEN ANALYSIS OF SLOSHING IN LIQUID-FILLED CONAINERS Mustafa Arafa Lcturr, Dpartmnt of Mchanical Dsign and Production Enginring, Cairo Univrsity, Cairo, Egypt mharafa@gmail.com, mharafa@yahoo.com

More information

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation. Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform

More information

Thermal and Structural Analysis of Roller Compacted Concrete (R.C.C) Dams by Finite Element Code

Thermal and Structural Analysis of Roller Compacted Concrete (R.C.C) Dams by Finite Element Code Australian Journal of Basic and Applid Scincs, 5(12): 2761-2767, 211 ISSN 1991-8178 hrmal and Structural Analysis of Rollr Compactd Concrt (R.C.C) Dams by Finit Elmnt Cod 1 Rahimi, A. and Noorzai, J. 1

More information

Rational Approximation for the one-dimensional Bratu Equation

Rational Approximation for the one-dimensional Bratu Equation Intrnational Journal of Enginring & Tchnology IJET-IJES Vol:3 o:05 5 Rational Approximation for th on-dimnsional Bratu Equation Moustafa Aly Soliman Chmical Enginring Dpartmnt, Th British Univrsity in

More information

DIFFERENTIAL EQUATION

DIFFERENTIAL EQUATION MD DIFFERENTIAL EQUATION Sllabus : Ordinar diffrntial quations, thir ordr and dgr. Formation of diffrntial quations. Solution of diffrntial quations b th mthod of sparation of variabls, solution of homognous

More information

A Comparative study of Load Capacity and Pressure Distribution of Infinitely wide Parabolic and Inclined Slider Bearings

A Comparative study of Load Capacity and Pressure Distribution of Infinitely wide Parabolic and Inclined Slider Bearings Procdings of th World Congrss on Enginring 2 Vol II WCE 2, Jun 3 - July 2, 2, London, U.K. A Comparativ study of Load Capacity and Prssur Distribution of Infinitly wid Parabolic and Inclind Slidr Barings

More information

arxiv: v1 [physics.comp-ph] 30 Jun 2016

arxiv: v1 [physics.comp-ph] 30 Jun 2016 On anisotropy function in crystal growth simulations using Lattic Boltzmann quation AMINA YOUNSI a,1, ALAIN CARTALADE a, a Dn DM2S, STMF, LMSF, CEA, Univrsité d Paris-Saclay, F-91191, Gif-sur-Yvtt, Franc.

More information

GAS FOIL BEARING ANALYSIS AND THE EFFECT OF BUMP FOIL THICKNESS ON ITS PERFORMANCE CHARACTERISTICS USING A NON-LINEAR MATRIX EQUATION SOLVER

GAS FOIL BEARING ANALYSIS AND THE EFFECT OF BUMP FOIL THICKNESS ON ITS PERFORMANCE CHARACTERISTICS USING A NON-LINEAR MATRIX EQUATION SOLVER GAS FOIL BEARING ANALYSIS AND THE EFFECT OF BUMP FOIL THICKNESS ON ITS PERFORMANCE CHARACTERISTICS USING A NON-LINEAR MATRIX EQUATION SOLVER T. Moasunp. Jamir 1)*, S. K. Kakoty 1), Karuna Kalita 1) 1)

More information

Effect of Combustion Heat Release on the Stability of Confined Boundary/mixing-layer Confluent flow

Effect of Combustion Heat Release on the Stability of Confined Boundary/mixing-layer Confluent flow Availabl onlin at www.scincdirct.com ScincDirct Procdia Enginring (4) www.lsvir.com/locat/procdia APISA4, 4 Asia-Pacific Intrnational Symposium on Arospac chnology, APISA4 Effct of Combustion Hat Rlas

More information

Trigonometric functions

Trigonometric functions Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,

More information

u 3 = u 3 (x 1, x 2, x 3 )

u 3 = u 3 (x 1, x 2, x 3 ) Lctur 23: Curvilinar Coordinats (RHB 8.0 It is oftn convnint to work with variabls othr than th Cartsian coordinats x i ( = x, y, z. For xampl in Lctur 5 w mt sphrical polar and cylindrical polar coordinats.

More information

Use of Proper Closure Equations in Finite Volume Discretization Schemes

Use of Proper Closure Equations in Finite Volume Discretization Schemes Us of ropr Closur Equations in Finit Volum Discrtization Schms 3 A. Ashrafizadh, M. Rzvani and B. Alinia K. N. Toosi Univrsity of Tchnology Iran 1. Introduction Finit Volum Mthod (FVM) is a popular fild

More information

Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a

Rotor Stationary Control Analysis Based on Coupling KdV Equation Finite Steady Analysis Liu Dalong1,a, Xu Lijuan2,a 204 Intrnational Confrnc on Computr Scinc and Elctronic Tchnology (ICCSET 204) Rotor Stationary Control Analysis Basd on Coupling KdV Equation Finit Stady Analysis Liu Dalong,a, Xu Lijuan2,a Dpartmnt of

More information

Construction of asymmetric orthogonal arrays of strength three via a replacement method

Construction of asymmetric orthogonal arrays of strength three via a replacement method isid/ms/26/2 Fbruary, 26 http://www.isid.ac.in/ statmath/indx.php?modul=prprint Construction of asymmtric orthogonal arrays of strngth thr via a rplacmnt mthod Tian-fang Zhang, Qiaoling Dng and Alok Dy

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

Dynamic analysis of a Timoshenko beam subjected to moving concentrated forces using the finite element method

Dynamic analysis of a Timoshenko beam subjected to moving concentrated forces using the finite element method Shock and Vibration 4 27) 459 468 459 IOS Prss Dynamic analysis of a Timoshnko bam subjctd to moving concntratd forcs using th finit lmnt mthod Ping Lou, Gong-lian Dai and Qing-yuan Zng School of Civil

More information

Nusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties

Nusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties Journal of Physics: Confrnc Sris OPEN ACCESS Nusslt numbr corrlations for simultanously dvloping laminar duct flows of liquids with tmpratur dpndnt proprtis To cit this articl: Stfano Dl Giudic t al 2014

More information

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA

NEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals

More information

Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem

Uniformly stable discontinuous Galerkin discretization and robust iterative solution methods for the Brinkman problem www.oaw.ac.at Uniformly stabl discontinuous Galrin discrtization and robust itrativ solution mtods for t Brinman problm Q. Hong, J. Kraus RICAM-Rport 2014-36 www.ricam.oaw.ac.at UNIFORMLY STABLE DISCONTINUOUS

More information

10. The Discrete-Time Fourier Transform (DTFT)

10. The Discrete-Time Fourier Transform (DTFT) Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w

More information

A nonequilibrium molecular dynamics simulation of evaporation

A nonequilibrium molecular dynamics simulation of evaporation Intrnational Confrnc Passiv and Low Enrgy Cooling 543 A nonquilibrium molcular dynamics simulation of vaporation Z.-J. Wang, M. Chn and Z.-Y. Guo Dpartmnt of Enginring Mchanics, Tsinghua Univrsity, Bijing

More information

Dynamic Characteristics Analysis of Blade of Fan Based on Ansys

Dynamic Characteristics Analysis of Blade of Fan Based on Ansys Powr and Enrgy Enginring Confrnc 1 Dynamic Charactristics Analysis of Blad of Fan Basd on Ansys Junji Zhou, Bo Liu, Dingbiao Wang, Xiaoqian li School of Chmical Enginring Zhngzhou Univrsity Scinc Road

More information

c 2007 Society for Industrial and Applied Mathematics

c 2007 Society for Industrial and Applied Mathematics SIAM J. NUMER. ANAL. Vol. 45, No. 3, pp. 1269 1286 c 2007 Socity for Industrial and Applid Mathmatics NEW FINITE ELEMENT METHODS IN COMPUTATIONAL FLUID DYNAMICS BY H (DIV) ELEMENTS JUNPING WANG AND XIU

More information

cycle that does not cross any edges (including its own), then it has at least

cycle that does not cross any edges (including its own), then it has at least W prov th following thorm: Thorm If a K n is drawn in th plan in such a way that it has a hamiltonian cycl that dos not cross any dgs (including its own, thn it has at last n ( 4 48 π + O(n crossings Th

More information

NONLINEAR ANALYSIS OF PLATE BENDING

NONLINEAR ANALYSIS OF PLATE BENDING NONLINEAR ANALYSIS OF PLATE BENDING CONTENTS Govrning Equations of th First-Ordr Shar Dformation thor (FSDT) Finit lmnt modls of FSDT Shar and mmbran locking Computr implmntation Strss calculation Numrical

More information

Large Scale Topology Optimization Using Preconditioned Krylov Subspace Recycling and Continuous Approximation of Material Distribution

Large Scale Topology Optimization Using Preconditioned Krylov Subspace Recycling and Continuous Approximation of Material Distribution Larg Scal Topology Optimization Using Prconditiond Krylov Subspac Rcycling and Continuous Approximation of Matrial Distribution Eric d Sturlr*, Chau L**, Shun Wang***, Glaucio Paulino** * Dpartmnt of Mathmatics,

More information

Symmetric Interior Penalty Galerkin Method for Elliptic Problems

Symmetric Interior Penalty Galerkin Method for Elliptic Problems Symmtric Intrior Pnalty Galrkin Mthod for Elliptic Problms Ykatrina Epshtyn and Béatric Rivièr Dpartmnt of Mathmatics, Univrsity of Pittsburgh, 3 Thackray, Pittsburgh, PA 56, U.S.A. Abstract This papr

More information

Actuator Disc Model Using a Modified Rhie-Chow/SIMPLE Pressure Correction Algorithm Rethore, Pierre-Elouan; Sørensen, Niels

Actuator Disc Model Using a Modified Rhie-Chow/SIMPLE Pressure Correction Algorithm Rethore, Pierre-Elouan; Sørensen, Niels Aalborg Univrsitt Actuator Disc Modl Using a Modifid Rhi-Chow/SIMLE rssur Corrction Algorithm Rthor, irr-elouan; Sørnsn, Nils ublishd in: EWEC 2008 Confrnc rocdings ublication dat: 2008 Documnt Vrsion

More information

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations

A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations www.oaw.ac.at A robust multigrid mtod for discontinuous Galrin discrtizations of Stos and linar lasticity quations Q. Hong, J. Kraus, J. Xu, L. Ziatanov RICAM-Rport 2013-19 www.ricam.oaw.ac.at A ROBUST

More information

The graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the

The graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th

More information

Direct Approach for Discrete Systems One-Dimensional Elements

Direct Approach for Discrete Systems One-Dimensional Elements CONTINUUM & FINITE ELEMENT METHOD Dirct Approach or Discrt Systms On-Dimnsional Elmnts Pro. Song Jin Par Mchanical Enginring, POSTECH Dirct Approach or Discrt Systms Dirct approach has th ollowing aturs:

More information

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals.

Background: We have discussed the PIB, HO, and the energy of the RR model. In this chapter, the H-atom, and atomic orbitals. Chaptr 7 Th Hydrogn Atom Background: W hav discussd th PIB HO and th nrgy of th RR modl. In this chaptr th H-atom and atomic orbitals. * A singl particl moving undr a cntral forc adoptd from Scott Kirby

More information

AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions

AerE 344: Undergraduate Aerodynamics and Propulsion Laboratory. Lab Instructions ArE 344: Undrgraduat Arodynamics and ropulsion Laboratory Lab Instructions Lab #08: Visualization of th Shock Wavs in a Suprsonic Jt by using Schlirn tchniqu Instructor: Dr. Hui Hu Dpartmnt of Arospac

More information

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim.

COHORT MBA. Exponential function. MATH review (part2) by Lucian Mitroiu. The LOG and EXP functions. Properties: e e. lim. MTH rviw part b Lucian Mitroiu Th LOG and EXP functions Th ponntial function p : R, dfind as Proprtis: lim > lim p Eponntial function Y 8 6 - -8-6 - - X Th natural logarithm function ln in US- log: function

More information

Apparent Power and Power Factor Measurement by Using FPGA-based Chip Considering Nonsinusoidal and Unbalanced Conditions

Apparent Power and Power Factor Measurement by Using FPGA-based Chip Considering Nonsinusoidal and Unbalanced Conditions Procdings of t 8t WE Intrnational Confrnc on Instrumntation, Masurmnt, Circuits and ystms pparnt Powr and Powr Factor Masurmnt by Using FPG-basd Cip Considring Nonsinusoidal and Unbalancd Conditions HU-CHEN

More information

Lagrangian Analysis of a Class of Quadratic Liénard-Type Oscillator Equations with Exponential-Type Restoring Force function

Lagrangian Analysis of a Class of Quadratic Liénard-Type Oscillator Equations with Exponential-Type Restoring Force function agrangian Analysis of a Class of Quadratic iénard-ty Oscillator Equations wit Eonntial-Ty Rstoring Forc function J. Akand, D. K. K. Adjaï,.. Koudaoun,Y. J. F. Komaou,. D. onsia. Dartmnt of Pysics, Univrsity

More information

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c.

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c. AP CALCULUS BC SUMMER ASSIGNMENT DO NOT SHOW YOUR WORK ON THIS! Complt ts problms during t last two wks of August. SHOW ALL WORK. Know ow to do ALL of ts problms, so do tm wll. Itms markd wit a * dnot

More information

Koch Fractal Boundary Single feed Circularly Polarized Microstrip Antenna

Koch Fractal Boundary Single feed Circularly Polarized Microstrip Antenna 1 Journal of Microwavs, Optolctronics and Elctromagntic Applications, Vol. 6, No. 2, Dcmbr 2007 406 Koch Fractal Boundary Singl fd Circularly Polarizd Microstrip Antnna P. Nagswara Rao and N. V. S.N Sarma

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

Intro to Nuclear and Particle Physics (5110)

Intro to Nuclear and Particle Physics (5110) Intro to Nuclar and Particl Physics (5110) March 09, 009 Frmi s Thory of Bta Dcay (continud) Parity Violation, Nutrino Mass 3/9/009 1 Final Stat Phas Spac (Rviw) Th Final Stat lctron and nutrino wav functions

More information

Electromagnetic Scattering Analysis of Arbitrarily Shaped Material Cylinder by FEM-BEM Method

Electromagnetic Scattering Analysis of Arbitrarily Shaped Material Cylinder by FEM-BEM Method NASA Tchnical Papr 3575 Elctromagntic Scattring Analysis of Arbitrarily Shapd Matrial Cylindr by FEM-BEM Mthod M. D. Dshpand VIGYAN, Inc. Hampton, Virginia C. R. Cockrll and C. J. Rddy Langly Rsarch Cntr

More information

A Sub-Optimal Log-Domain Decoding Algorithm for Non-Binary LDPC Codes

A Sub-Optimal Log-Domain Decoding Algorithm for Non-Binary LDPC Codes Procdings of th 9th WSEAS Intrnational Confrnc on APPLICATIONS of COMPUTER ENGINEERING A Sub-Optimal Log-Domain Dcoding Algorithm for Non-Binary LDPC Cods CHIRAG DADLANI and RANJAN BOSE Dpartmnt of Elctrical

More information

Linear Non-Gaussian Structural Equation Models

Linear Non-Gaussian Structural Equation Models IMPS 8, Durham, NH Linar Non-Gaussian Structural Equation Modls Shohi Shimizu, Patrik Hoyr and Aapo Hyvarinn Osaka Univrsity, Japan Univrsity of Hlsinki, Finland Abstract Linar Structural Equation Modling

More information

Definition of Ablation testcase

Definition of Ablation testcase Dfinition of Ablation tstcas sris #3 5 t Ablation Worksop Lxington, KY Tom van Ekln LMS-Samtc, Blgium Jan Lacaud UARC/Univ. of California Santa Cruz, USA Alxandr Martin Univrsity of Kntucky, USA Ioana

More information

Developments in Geomathematics 5

Developments in Geomathematics 5 ~~": ~ L " r. :.. ~,.!.-. r,:... I Rprintd from I Dvlopmnts in Gomathmatics 5 Procdings of th Intrnational Symposium on Variational Mthods in ' Goscincs hld at th Univrsity of Oklahoma, Norman, Oklahoma,

More information

Derivation of Solution for Elliptical Elastohydrodynamic. Contact Patches with Side-Slip and its Application to a. Continuously Variable Transmission

Derivation of Solution for Elliptical Elastohydrodynamic. Contact Patches with Side-Slip and its Application to a. Continuously Variable Transmission T rport committ for Cristopr William Scnidr Crtifis tat tis is t approvd vrsion of t following rport: Drivation of Solution for Elliptical Elastoydrodynamic Contact Patcs wit Sid-Slip and its Application

More information

Another view for a posteriori error estimates for variational inequalities of the second kind

Another view for a posteriori error estimates for variational inequalities of the second kind Accptd by Applid Numrical Mathmatics in July 2013 Anothr viw for a postriori rror stimats for variational inqualitis of th scond kind Fi Wang 1 and Wimin Han 2 Abstract. In this papr, w giv anothr viw

More information

( ) Abstract. 2 FEDSS method basic relationships. 1 Introduction. 2.1 Tensorial formulation

( ) Abstract. 2 FEDSS method basic relationships. 1 Introduction. 2.1 Tensorial formulation Displacmnt basd continuous strss rcovry procdur, Mijuca D, Brkoviæ M. and Draškoviæ Z., Advancs in Finit Elmnt Tchnology, ISBN 0 948749 4, Ed. B.H.V.Topping, Civil Comp Prss, 7-34 (996). Abstract In this

More information

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014 Lecture 20: Transition State Theory. ERD: 25.14

University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2014 Lecture 20: Transition State Theory. ERD: 25.14 Univrsity of Wasinton Dpartmnt of Cmistry Cmistry 453 Wintr Quartr 04 Lctur 0: Transition Stat Tory. ERD: 5.4. Transition Stat Tory Transition Stat Tory (TST) or ctivatd Complx Tory (CT) is a raction mcanism

More information

Recursive Estimation of Dynamic Time-Varying Demand Models

Recursive Estimation of Dynamic Time-Varying Demand Models Intrnational Confrnc on Computr Systms and chnologis - CompSysch 06 Rcursiv Estimation of Dynamic im-varying Dmand Modls Alxandr Efrmov Abstract: h papr prsnts an implmntation of a st of rcursiv algorithms

More information

Finite Strain Elastic-Viscoplastic Model

Finite Strain Elastic-Viscoplastic Model Finit Strain Elastic-Viscoplastic Modl Pinksh Malhotra Mchanics of Solids,Brown Univrsity Introduction Th main goal of th projct is to modl finit strain rat-dpndnt plasticity using a modl compatibl for

More information

Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing

Numerical considerations regarding the simulation of an aircraft in the approaching phase for landing INCAS BULLETIN, Volum, Numbr 1/ 1 Numrical considrations rgarding th simulation of an aircraft in th approaching phas for landing Ionl Cristinl IORGA ionliorga@yahoo.com Univrsity of Craiova, Alxandru

More information

Supplementary Materials

Supplementary Materials 6 Supplmntary Matrials APPENDIX A PHYSICAL INTERPRETATION OF FUEL-RATE-SPEED FUNCTION A truck running on a road with grad/slop θ positiv if moving up and ngativ if moving down facs thr rsistancs: arodynamic

More information

Learning Spherical Convolution for Fast Features from 360 Imagery

Learning Spherical Convolution for Fast Features from 360 Imagery Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr

More information

CHAPTER 2 LAGRANGIAN AND EULERIAN FINITE ELEMENTS IN ONE DIMENSION

CHAPTER 2 LAGRANGIAN AND EULERIAN FINITE ELEMENTS IN ONE DIMENSION CHAPTER 2 LAGRANGIAN AND EULERIAN FINITE ELEMENTS IN ONE DIMENSION by Td Blytschko Northwstrn Univrsity @ Copyright 1997 2.1 Introduction In this chaptr, th quations for on-dimnsional modls of nonlinar

More information

TOPOLOGY DESIGN OF STRUCTURE LOADED BY EARTHQUAKE. Vienna University of Technology

TOPOLOGY DESIGN OF STRUCTURE LOADED BY EARTHQUAKE. Vienna University of Technology Bluchr Mchanical Enginring Procdings May 2014, vol. 1, num. 1 www.procdings.bluchr.com.br/vnto/10wccm TOPOLOGY DESIG OF STRUCTURE LOADED BY EARTHQUAKE P. Rosko 1 1 Cntr of Mchanics and Structural Dynamics,

More information

Reparameterization and Adaptive Quadrature for the Isogeometric Discontinuous Galerkin Method

Reparameterization and Adaptive Quadrature for the Isogeometric Discontinuous Galerkin Method Rparamtrization and Adaptiv Quadratur for th Isogomtric Discontinuous Galrkin Mthod Agns Silr, Brt Jüttlr 2 Doctoral Program Computational Mathmatics 2 Institut of Applid Gomtry Johanns Kplr Univrsity

More information