The Immersed Interface Method
|
|
- Tobias Hoover
- 5 years ago
- Views:
Transcription
1 The Immersed Interface Method Numerical Solutions of PDEs Involving Interfaces and Irregular Domains Zhiiin Li Kazufumi Ito North Carolina State University Raleigh, North Carolina Society for Industrial and Applied Mathematics Philadelphia
2 Preface xv Introduction A one-dimensional model problem A two-dimensional example of heat propagation in a heterogeneous material Examples of irregular domains and free boundary problems The scope of the monograph and the methodology Jump conditions The choice of grids A minireview of some popular finite difference methods for interface problems The smoothing method for discontinuous coefficients The harmonic averaging for discontinuous coefficients Peskin's immersed boundary (IB) method Numerical methods based on integral equations The ghost fluid method Finite difference and finite volume methods Conventions and notation Cartesian grids Limiting values and jump conditions The local coordinates Interface representations What is the 1IM? 20 The IIM for One-Dimensional Elliptic Interface Problems Reformulating the problem using the jump conditions The IIM for the simple one-dimensional model equation The derivation of the finite difference scheme at an irregular grid point The IIM for general one-dimensional elliptic interface problems The error analysis of the IIM for one-dimensional interface problems One-dimensional numerical examples and a comparison with other methods 30 IX
3 The IIM for Two-Dimensional Elliptic Interface Problems Interface relations for two-dimensional elliptic interface problems The finite difference scheme of the IIM in two dimensions The 6-point finite difference stencil at irregular grid points The fast Poisson solver for problems with only singular sources Enforcing the discrete maximum principle Choosing the finite difference stencil Solving the optimization problem The error analysis of the maximum principle preserving scheme Existence of the solution to the optimization problem The proof of the convergence of the finite difference scheme Some numerical examples for two-dimensional elliptic interface problems Algorithm efficiency analysis Multigrid solvers for large jump ratios 53 The IIM for Three-Dimensional Elliptic Interface Problems A local coordinate system in three dimensions Interface relations for three-dimensional elliptic interface problems The finite difference scheme of the IIM in three dimensions Finite difference equations at regular grid points Computing the orthogonal projection in a three-dimensional Cartesian grid Setting up a local coordinate system using a level set function The bilinear interpolation in three dimensions Deriving the finite difference equation at an irregular grid point Computing surface derivatives of interface quantities in three dimensions The 10-point finite difference stencil at irregular grid points The maximum principle preserving scheme in three dimensions Solving the finite difference equations using an AMG solver A numerical example for a three-dimensional elliptic interface problem 71 Removing Source Singularities for Certain Interface Problems Eliminating source singularities using level set functions: The Theory The finite difference scheme using the new formulation The extension of jump conditions along the normal lines 75
4 xi The orthogonal projections in Cartesian and polar coordinates in two dimensions The discretization strategy using the transformation An outline of the algorithm of removing source singularities A closed formula for the correction terms Computing the gradient using the new formulation An example of removing source singularities Removing source singularities for variable coefficients Orthogonal projections and extensions in spherical coordinates Augmented Strategies The augmented technique for elliptic interface problems The augmented variable for the elliptic interface problems 90.2 The discrete system of equations in matrix-vector form The least squares interpolation scheme from a Cartesian grid to an interface 94.4 Invertibility of the Schur complement system 97.5 A preconditioner for the Schur complement system 98.6 Numerical experiments and analysis of the fast IIM The augmented method for generalized Helmholtz equations on irregular domains An example of the augmented approach for Poisson equations on irregular domains The Fourth-Order IIM Two-point boundary value problems The constant coefficient case Ill General boundary conditions Ill The smooth variable coefficient case The piecewise constant coefficient case Two-dimensional cases The fourth-order compact central finite difference method Neumann boundary conditions The fourth-order method for Poisson equations on irregular domains Projections and a fourth-order polynomial interpolation The fourth-order method for heat equations on irregular domains The fourth-order method for PDEs with variable coefficient on irregular domains 127
5 xii Contents The fourth-order method for interface problems The fourth-order method for heat equations with interfaces The fourth-order methods for three dimensional cases The fourth-order scheme for problems on irregular domains in three dimensions The fourth-order scheme for three-dimensional interface problems The preconditioned subspace iteration method The irregular domain case The interface case Numerical experiments The irregular domain case Examples for eigenvalues and eigenfunctions in a circular domain Results for the variable coefficient case Results for the interface problem An eigenvalue problem with an interface The well-posedness and the convergence rate Convergence rate The Immersed Finite Element Methods The IFEM for one-dimensional interface problems New basis functions satisfying the jump conditions The interpolation functions in the one-dimensional IFEM space The convergence analysis for the one-dimensional IFEM A numerical example of one-dimensional IFEM The weak form of two-dimensional elliptic interface problems A nonconforming IFE space and analysis Local basis functions on an interface element The nonconforming IFE space Approximation properties of the nonconforming IFE space A nonconforming IFEM A conforming IFE space and analysis The conforming local basis functions on an interface element A conforming IFE space Approximation properties of the conforming IFE space A numerical example and analysis for IFEMs Numerical results for the conforming IFEM A comparison with the finite element method with added nodes IFEM for problems with nonhomogeneous jump conditions 186
6 xiii 9 The IIM for Parabolic Interface Problems The IIM for one-dimensional heat equations with fixed interfaces The IIM for one-dimensional moving interface problems The modified Crank-Nicholson scheme Dealing with grid crossing The discretizations of u x and (fiu x ) x near the interface Computing interface quantities "' Solving the resulting nonlinear system of equations Validation of the algorithm for a one-dimensional moving interface problem The modified ADI method for heat equations with discontinuities The modified ADI scheme Determining the spatial correction terms Decomposing the jump condition in the coordinate directions The local truncation error analysis for the ADI method A numerical example of the modified ADI method The IIM for diffusion and advection equations Determining the finite difference coefficients for the diffusion term Determining the finite difference coefficients for the advection term The IIM for Stokes and Navier-Stokes Equations The derivation of the jump conditions for Stokes and Navier-Stokes equations The IIM for Stokes equations with singular sources: The membrane model The force density of the elastic membrane model Solving the Poisson equation for the pressure Solving the Poisson equations for the velocity (u,v) Evolving the interface using an explicit method Evolving the interface using an implicit method The validation of the IIM for moving elastic membranes The IIM for Stokes equations with singular sources: The surface tension model An augmented approach for Stokes equations with discontinuous viscosity The augmented algorithm for Stokes equations The validation of the augmented method for Stokes equations An augmented approach for pressure boundary conditions Computing the Laplacian of the velocity along a boundary for a nonslip boundary condition 249
7 xiv Contents 10.6 The IIM for Navier-Stokes equations with singular sources Additional interface relations The modified finite difference method for Navier-Stokes equations with interfaces Determining the correction terms Correction terms to the projection method Further corrections near the boundary and the interface " Comparisons and validation of the IIM for Navier-Stokes equations with interfaces Some Applications of the IIM The framework coupling the IIM with evolution schemes The front-tracking method Coupling the level set method with the IIM Orthogonal projections and the bilinear interpolation Velocity extension along normal directions Reconstructing the interface locally from a level set function The hybrid IIM-level set method for the Hele-Shaw flow Dynamic stability of the Hele-Shaw flow The IIM for the Hele-Shaw flow Numerical experiments of the Hele-Shaw flow Simulations of Stefan problems and crystal growth A modified Crank-Nicolson discretization The modified ADI method for Stefan problems Numerical simulations of the Stefan problem An application to an inverse problem of shape identification An outline of the algorithm for the inverse problem Identifying several minima Numerical examples of shape identification Applications to nonlinear interface problems The substitution method Computing p and its derivatives Numerical experiments of MR fluids with particles Other methods related to the IIM The IIM for hyperbolic systems of PDEs The explicit jump immersed interface method (EJIIM) The high-order matched interface and boundary method Future directions 309 Bibliography 311 Index 331
Index. C m (Ω), 141 L 2 (Ω) space, 143 p-th order, 17
Bibliography [1] J. Adams, P. Swarztrauber, and R. Sweet. Fishpack: Efficient Fortran subprograms for the solution of separable elliptic partial differential equations. http://www.netlib.org/fishpack/.
More informationContents. I The Basic Framework for Stationary Problems 1
page v Preface xiii I The Basic Framework for Stationary Problems 1 1 Some model PDEs 3 1.1 Laplace s equation; elliptic BVPs... 3 1.1.1 Physical experiments modeled by Laplace s equation... 5 1.2 Other
More informationInvestigation of cross flow over a circular cylinder at low Re using the Immersed Boundary Method (IBM)
Computational Methods and Experimental Measurements XVII 235 Investigation of cross flow over a circular cylinder at low Re using the Immersed Boundary Method (IBM) K. Rehman Department of Mechanical Engineering,
More informationOutline. Level Set Methods. For Inverse Obstacle Problems 4. Introduction. Introduction. Martin Burger
For Inverse Obstacle Problems Martin Burger Outline Introduction Optimal Geometries Inverse Obstacle Problems & Shape Optimization Sensitivity Analysis based on Gradient Flows Numerical Methods University
More informationComputational Fluid Dynamics for Engineers
Tuncer Cebeci Jian P. Shao Fassi Kafyeke Eric Laurendeau Computational Fluid Dynamics for Engineers From Panel to Navier-Stokes Methods with Computer Programs With 152 Figures, 19 Tables, 84 Problems and
More informationcuibm A GPU Accelerated Immersed Boundary Method
cuibm A GPU Accelerated Immersed Boundary Method S. K. Layton, A. Krishnan and L. A. Barba Corresponding author: labarba@bu.edu Department of Mechanical Engineering, Boston University, Boston, MA, 225,
More informationPartial Differential Equations
Simulation in Computer Graphics Partial Differential Equations Matthias Teschner Computer Science Department University of Freiburg Motivation various dynamic effects and physical processes are described
More informationCS205b/CME306. Lecture 9
CS205b/CME306 Lecture 9 1 Convection Supplementary Reading: Osher and Fedkiw, Sections 3.3 and 3.5; Leveque, Sections 6.7, 8.3, 10.2, 10.4. For a reference on Newton polynomial interpolation via divided
More informationCommunications in Applied Mathematics and Computational Science
Communications in Applied Mathematics and Computational Science Volume 1 No. 1 2006 A COMPARISON OF THE EXTENDED FINITE ELEMENT METHOD WITH THE IMMERSED INTERFACE METHOD FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS
More informationAn Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods
Commun. Comput. Phys. doi: 10.4208/cicp.070211.150811s Vol. 12, No. 2, pp. 515-527 August 2012 An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods Zhilin Li 1, and Peng Song 2
More informationThe 3D DSC in Fluid Simulation
The 3D DSC in Fluid Simulation Marek K. Misztal Informatics and Mathematical Modelling, Technical University of Denmark mkm@imm.dtu.dk DSC 2011 Workshop Kgs. Lyngby, 26th August 2011 Governing Equations
More informationFOURTH ORDER COMPACT FORMULATION OF STEADY NAVIER-STOKES EQUATIONS ON NON-UNIFORM GRIDS
International Journal of Mechanical Engineering and Technology (IJMET Volume 9 Issue 10 October 2018 pp. 179 189 Article ID: IJMET_09_10_11 Available online at http://www.iaeme.com/ijmet/issues.asp?jtypeijmet&vtype9&itype10
More informationModule 1: Introduction to Finite Difference Method and Fundamentals of CFD Lecture 13: The Lecture deals with:
The Lecture deals with: Some more Suggestions for Improvement of Discretization Schemes Some Non-Trivial Problems with Discretized Equations file:///d /chitra/nptel_phase2/mechanical/cfd/lecture13/13_1.htm[6/20/2012
More informationNIA CFD Seminar, October 4, 2011 Hyperbolic Seminar, NASA Langley, October 17, 2011
NIA CFD Seminar, October 4, 2011 Hyperbolic Seminar, NASA Langley, October 17, 2011 First-Order Hyperbolic System Method If you have a CFD book for hyperbolic problems, you have a CFD book for all problems.
More informationsmooth coefficients H. Köstler, U. Rüde
A robust multigrid solver for the optical flow problem with non- smooth coefficients H. Köstler, U. Rüde Overview Optical Flow Problem Data term and various regularizers A Robust Multigrid Solver Galerkin
More informationParallel High-Order Geometric Multigrid Methods on Adaptive Meshes for Highly Heterogeneous Nonlinear Stokes Flow Simulations of Earth s Mantle
ICES Student Forum The University of Texas at Austin, USA November 4, 204 Parallel High-Order Geometric Multigrid Methods on Adaptive Meshes for Highly Heterogeneous Nonlinear Stokes Flow Simulations of
More informationUnstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications
Unstructured Mesh Generation for Implicit Moving Geometries and Level Set Applications Per-Olof Persson (persson@mit.edu) Department of Mathematics Massachusetts Institute of Technology http://www.mit.edu/
More informationIll-Posed Problems with A Priori Information
INVERSE AND ILL-POSED PROBLEMS SERIES Ill-Posed Problems with A Priori Information V.V.Vasin andalageev HIV SPIII Utrecht, The Netherlands, 1995 CONTENTS Introduction 1 CHAPTER 1. UNSTABLE PROBLEMS 1 Base
More informationSecond International Workshop on Scientific Computing and Applications. Kananaskis, Canada, May 28 - June 1, 2000
Second International Workshop on Scientific Computing and Applications. Kananaskis, Canada, May 28 - June 1, 2000 Program May 28 (Sunday) 19:00-21:00 Registration and reception Session Chairman: Y. Wong
More informationAn introduction to mesh generation Part IV : elliptic meshing
Elliptic An introduction to mesh generation Part IV : elliptic meshing Department of Civil Engineering, Université catholique de Louvain, Belgium Elliptic Curvilinear Meshes Basic concept A curvilinear
More informationStudies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimization
Studies of the Continuous and Discrete Adjoint Approaches to Viscous Automatic Aerodynamic Shape Optimization Siva Nadarajah Antony Jameson Stanford University 15th AIAA Computational Fluid Dynamics Conference
More informationAdarsh Krishnamurthy (cs184-bb) Bela Stepanova (cs184-bs)
OBJECTIVE FLUID SIMULATIONS Adarsh Krishnamurthy (cs184-bb) Bela Stepanova (cs184-bs) The basic objective of the project is the implementation of the paper Stable Fluids (Jos Stam, SIGGRAPH 99). The final
More informationA fast solver for the Stokes equations with distributed forces in complex geometries 1
A fast solver for the Stokes equations with distributed forces in complex geometries George Biros, Lexing Ying, and Denis Zorin Courant Institute of Mathematical Sciences, New York University, New York
More informationSELECTIVE ALGEBRAIC MULTIGRID IN FOAM-EXTEND
Student Submission for the 5 th OpenFOAM User Conference 2017, Wiesbaden - Germany: SELECTIVE ALGEBRAIC MULTIGRID IN FOAM-EXTEND TESSA UROIĆ Faculty of Mechanical Engineering and Naval Architecture, Ivana
More informationMATLAB. Advanced Mathematics and Mechanics Applications Using. Third Edition. David Halpern University of Alabama CHAPMAN & HALL/CRC
Advanced Mathematics and Mechanics Applications Using MATLAB Third Edition Howard B. Wilson University of Alabama Louis H. Turcotte Rose-Hulman Institute of Technology David Halpern University of Alabama
More informationCurve and Surface Fitting with Splines. PAUL DIERCKX Professor, Computer Science Department, Katholieke Universiteit Leuven, Belgium
Curve and Surface Fitting with Splines PAUL DIERCKX Professor, Computer Science Department, Katholieke Universiteit Leuven, Belgium CLARENDON PRESS OXFORD 1995 - Preface List of Figures List of Tables
More informationAn Isoparametric Finite Element Method for Elliptic Interface Problems with Nonhomogeneous Jump Conditions
An Isoparametric Finite Element Method for Elliptic Interface Problems with Nonhomogeneous Jump Conditions XUFA FANG Department of Mathematics Zheiang University 38 Zheda Road, 37 Hangzhou CHINA woshimethod@63.com
More informationContents. I Basics 1. Copyright by SIAM. Unauthorized reproduction of this article is prohibited.
page v Preface xiii I Basics 1 1 Optimization Models 3 1.1 Introduction... 3 1.2 Optimization: An Informal Introduction... 4 1.3 Linear Equations... 7 1.4 Linear Optimization... 10 Exercises... 12 1.5
More informationA novel model for biolm growth and its resolution by using the hybrid immersed interface-level set method
A novel model for biolm growth and its resolution by using the hybrid immersed interface-level set method Juan A. Asenjo & Carlos Conca Applied Mathematics Group - Basic Sciences Department - University
More informationA fast finite difference method for biharmonic equations on irregular domains
A fast finite difference method for biharmonic equations on irregular domains Guo Chen Zhilin Li Ping Lin Abstract Biharmonic equations have many applications, especially in fluid and solid mechanics,
More informationA Sharp Interface Cartesian Grid Method for Simulating Flows with Complex Moving Boundaries
Journal of Computational Physics 174, 345 380 (2001) doi:10.1006/jcph.2001.6916, available online at http://www.idealibrary.com on A Sharp Interface Cartesian Grid Method for Simulating Flows with Complex
More informationData-Driven Modeling. Scientific Computation J. NATHAN KUTZ OXPORD. Methods for Complex Systems & Big Data
Data-Driven Modeling & Scientific Computation Methods for Complex Systems & Big Data J. NATHAN KUTZ Department ofapplied Mathematics University of Washington OXPORD UNIVERSITY PRESS Contents Prolegomenon
More informationEditorial Coupled Numerical Methods in Engineering Analysis
Mathematical Problems in Engineering Volume 2011, Article ID 436978, 4 pages doi:10.1155/2011/436978 Editorial Coupled Numerical Methods in Engineering Analysis Delfim Soares Jr., 1 Otto von Estorff, 2
More informationCUDA. Fluid simulation Lattice Boltzmann Models Cellular Automata
CUDA Fluid simulation Lattice Boltzmann Models Cellular Automata Please excuse my layout of slides for the remaining part of the talk! Fluid Simulation Navier Stokes equations for incompressible fluids
More informationMultigrid Solvers in CFD. David Emerson. Scientific Computing Department STFC Daresbury Laboratory Daresbury, Warrington, WA4 4AD, UK
Multigrid Solvers in CFD David Emerson Scientific Computing Department STFC Daresbury Laboratory Daresbury, Warrington, WA4 4AD, UK david.emerson@stfc.ac.uk 1 Outline Multigrid: general comments Incompressible
More informationAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R. Elliot English, Linhai Qiu, Yue Yu, Ronald Fedkiw Stanford University, 353 Serra Mall Room 27, Stanford,
More informationThe Development of a Navier-Stokes Flow Solver with Preconditioning Method on Unstructured Grids
Proceedings of the International MultiConference of Engineers and Computer Scientists 213 Vol II, IMECS 213, March 13-15, 213, Hong Kong The Development of a Navier-Stokes Flow Solver with Preconditioning
More informationNumerical methods for volume preserving image registration
Numerical methods for volume preserving image registration SIAM meeting on imaging science 2004 Eldad Haber with J. Modersitzki haber@mathcs.emory.edu Emory University Volume preserving IR p.1/?? Outline
More informationComputational Fluid Dynamics - Incompressible Flows
Computational Fluid Dynamics - Incompressible Flows March 25, 2008 Incompressible Flows Basis Functions Discrete Equations CFD - Incompressible Flows CFD is a Huge field Numerical Techniques for solving
More informationA 3D VOF model in cylindrical coordinates
A 3D VOF model in cylindrical coordinates Marmar Mehrabadi and Markus Bussmann Department of Mechanical and Industrial Engineering, University of Toronto Recently, volume of fluid (VOF) methods have improved
More informationSimulation in Computer Graphics. Particles. Matthias Teschner. Computer Science Department University of Freiburg
Simulation in Computer Graphics Particles Matthias Teschner Computer Science Department University of Freiburg Outline introduction particle motion finite differences system of first order ODEs second
More informationDevelopment of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics
Development of an Integrated Computational Simulation Method for Fluid Driven Structure Movement and Acoustics I. Pantle Fachgebiet Strömungsmaschinen Karlsruher Institut für Technologie KIT Motivation
More informationAn Interface-fitted Mesh Generator and Polytopal Element Methods for Elliptic Interface Problems
An Interface-fitted Mesh Generator and Polytopal Element Methods for Elliptic Interface Problems Long Chen University of California, Irvine chenlong@math.uci.edu Joint work with: Huayi Wei (Xiangtan University),
More informationSOLVING PARTIAL DIFFERENTIAL EQUATIONS ON POINT CLOUDS
SOLVING PARTIAL DIFFERENTIAL EQUATIONS ON POINT CLOUDS JIAN LIANG AND HONGKAI ZHAO Abstract. In this paper we present a general framework for solving partial differential equations on manifolds represented
More informationA MULTIGRID ALGORITHM FOR IMMERSED INTERFACE PROBLEMS. Loyce Adams 1. University of Washington SUMMARY
A MULTIGRID ALGORITHM FOR IMMERSED INTERFACE PROBLEMS Loyce Adams Dept. of Applied Mathematics University of Washington SUMMARY Many physical problems involve interior interfaces across which the coecients
More informationALE Seamless Immersed Boundary Method with Overset Grid System for Multiple Moving Objects
Tenth International Conference on Computational Fluid Dynamics (ICCFD10), Barcelona,Spain, July 9-13, 2018 ICCFD10-047 ALE Seamless Immersed Boundary Method with Overset Grid System for Multiple Moving
More informationC. A. D. Fraga Filho 1,2, D. F. Pezzin 1 & J. T. A. Chacaltana 1. Abstract
Advanced Computational Methods and Experiments in Heat Transfer XIII 15 A numerical study of heat diffusion using the Lagrangian particle SPH method and the Eulerian Finite-Volume method: analysis of convergence,
More informationAn Embedded Boundary Method with Adaptive Mesh Refinements
An Embedded Boundary Method with Adaptive Mesh Refinements Marcos Vanella and Elias Balaras 8 th World Congress on Computational Mechanics, WCCM8 5 th European Congress on Computational Methods in Applied
More informationMoving Interface Problems: Methods & Applications Tutorial Lecture II
Moving Interface Problems: Methods & Applications Tutorial Lecture II Grétar Tryggvason Worcester Polytechnic Institute Moving Interface Problems and Applications in Fluid Dynamics Singapore National University,
More informationHigh-Order Finite Difference Schemes for computational MHD
High-Order Finite Difference Schemes for computational MHD A. Mignone 1, P. Tzeferacos 1 and G. Bodo 2 [1] Dipartimento di Fisica Generale, Turin University, ITALY [2] INAF Astronomic Observatory of Turin,,
More informationLevel set methods Formulation of Interface Propagation Boundary Value PDE Initial Value PDE Motion in an externally generated velocity field
Level Set Methods Overview Level set methods Formulation of Interface Propagation Boundary Value PDE Initial Value PDE Motion in an externally generated velocity field Convection Upwind ddifferencingi
More informationNumerical Analysis of Shock Tube Problem by using TVD and ACM Schemes
Numerical Analysis of Shock Tube Problem by using TVD and Schemes Dr. Mukkarum Husain, Dr. M. Nauman Qureshi, Syed Zaid Hasany IST Karachi, Email: mrmukkarum@yahoo.com Abstract Computational Fluid Dynamics
More informationA Toolbox of Level Set Methods
A Toolbox of Level Set Methods Ian Mitchell Department of Computer Science University of British Columbia http://www.cs.ubc.ca/~mitchell mitchell@cs.ubc.ca research supported by the Natural Science and
More informationLattice Boltzmann with CUDA
Lattice Boltzmann with CUDA Lan Shi, Li Yi & Liyuan Zhang Hauptseminar: Multicore Architectures and Programming Page 1 Outline Overview of LBM An usage of LBM Algorithm Implementation in CUDA and Optimization
More informationApplication of Finite Volume Method for Structural Analysis
Application of Finite Volume Method for Structural Analysis Saeed-Reza Sabbagh-Yazdi and Milad Bayatlou Associate Professor, Civil Engineering Department of KNToosi University of Technology, PostGraduate
More informationBiomagnetic inverse problems:
Biomagnetic inverse problems: Magnetic resonance electrical property tomography (MREPT) and magnetoencephalography (MEG) 2018 Aug. 16 The University of Tokyo Takaaki Nara 1 Contents Measurement What is
More informationModule 1: Introduction to Finite Difference Method and Fundamentals of CFD Lecture 6:
file:///d:/chitra/nptel_phase2/mechanical/cfd/lecture6/6_1.htm 1 of 1 6/20/2012 12:24 PM The Lecture deals with: ADI Method file:///d:/chitra/nptel_phase2/mechanical/cfd/lecture6/6_2.htm 1 of 2 6/20/2012
More informationA higher-order finite volume method with collocated grid arrangement for incompressible flows
Computational Methods and Experimental Measurements XVII 109 A higher-order finite volume method with collocated grid arrangement for incompressible flows L. Ramirez 1, X. Nogueira 1, S. Khelladi 2, J.
More informationEfficient Tridiagonal Solvers for ADI methods and Fluid Simulation
Efficient Tridiagonal Solvers for ADI methods and Fluid Simulation Nikolai Sakharnykh - NVIDIA San Jose Convention Center, San Jose, CA September 21, 2010 Introduction Tridiagonal solvers very popular
More informationRealistic Animation of Fluids
1 Realistic Animation of Fluids Nick Foster and Dimitris Metaxas Presented by Alex Liberman April 19, 2005 2 Previous Work Used non physics-based methods (mostly in 2D) Hard to simulate effects that rely
More informationFlow Structures Extracted from Visualization Images: Vector Fields and Topology
Flow Structures Extracted from Visualization Images: Vector Fields and Topology Tianshu Liu Department of Mechanical & Aerospace Engineering Western Michigan University, Kalamazoo, MI 49008, USA We live
More informationAn adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids R. Elliot English, Linhai Qiu,YueYu, Ronald Fedkiw Stanford University, 353 Serra Mall Room 27, Stanford, CA
More informationLarge-Scale Simulations on Parallel Computers!
http://users.wpi.edu/~gretar/me612.html! Large-Scale Simulations on Parallel Computers! Grétar Tryggvason! Spring 2010! Outline!!Basic Machine configurations!!parallelization!!the Message Passing Interface
More information1.2 Numerical Solutions of Flow Problems
1.2 Numerical Solutions of Flow Problems DIFFERENTIAL EQUATIONS OF MOTION FOR A SIMPLIFIED FLOW PROBLEM Continuity equation for incompressible flow: 0 Momentum (Navier-Stokes) equations for a Newtonian
More informationMODERN FACTOR ANALYSIS
MODERN FACTOR ANALYSIS Harry H. Harman «ö THE pigj UNIVERSITY OF CHICAGO PRESS Contents LIST OF ILLUSTRATIONS GUIDE TO NOTATION xv xvi Parti Foundations of Factor Analysis 1. INTRODUCTION 3 1.1. Brief
More informationA New Incompressibility Discretization for a Hybrid Particle MAC Grid Representation with Surface Tension
A New Incompressibility Discretization for a Hybrid Particle MAC Grid Representation with Surface Tension Wen Zheng, Bo Zhu, Byungmoon Kim, Ronald Fedkiw Stanford University, 353 Serra Mall Room 207, Stanford,
More informationParameterization of Meshes
2-Manifold Parameterization of Meshes What makes for a smooth manifold? locally looks like Euclidian space collection of charts mutually compatible on their overlaps form an atlas Parameterizations are
More informationFrom Hyperbolic Diffusion Scheme to Gradient Method: Implicit Green-Gauss Gradients for Unstructured Grids
Preprint accepted in Journal of Computational Physics. https://doi.org/10.1016/j.jcp.2018.06.019 From Hyperbolic Diffusion Scheme to Gradient Method: Implicit Green-Gauss Gradients for Unstructured Grids
More informationAMS527: Numerical Analysis II
AMS527: Numerical Analysis II A Brief Overview of Finite Element Methods Xiangmin Jiao SUNY Stony Brook Xiangmin Jiao SUNY Stony Brook AMS527: Numerical Analysis II 1 / 25 Overview Basic concepts Mathematical
More information1.7.1 Laplacian Smoothing
1.7.1 Laplacian Smoothing 320491: Advanced Graphics - Chapter 1 434 Theory Minimize energy functional total curvature estimate by polynomial-fitting non-linear (very slow!) 320491: Advanced Graphics -
More informationModeling and simulation the incompressible flow through pipelines 3D solution for the Navier-Stokes equations
Modeling and simulation the incompressible flow through pipelines 3D solution for the Navier-Stokes equations Daniela Tudorica 1 (1) Petroleum Gas University of Ploiesti, Department of Information Technology,
More informationSolving partial differential equations using the NAG Library
Solving partial differential equations using the NAG Library 1. Introduction Jeremy Walton The Numerical Algorithms Group, Ltd. Wilkinson House, Jordan Hill Road Oxford OX2 8DR, United Kingdom A partial
More informationFinal Report. Discontinuous Galerkin Compressible Euler Equation Solver. May 14, Andrey Andreyev. Adviser: Dr. James Baeder
Final Report Discontinuous Galerkin Compressible Euler Equation Solver May 14, 2013 Andrey Andreyev Adviser: Dr. James Baeder Abstract: In this work a Discontinuous Galerkin Method is developed for compressible
More informationA High-Order Accurate Unstructured GMRES Solver for Poisson s Equation
A High-Order Accurate Unstructured GMRES Solver for Poisson s Equation Amir Nejat * and Carl Ollivier-Gooch Department of Mechanical Engineering, The University of British Columbia, BC V6T 1Z4, Canada
More informationDebojyoti Ghosh. Adviser: Dr. James Baeder Alfred Gessow Rotorcraft Center Department of Aerospace Engineering
Debojyoti Ghosh Adviser: Dr. James Baeder Alfred Gessow Rotorcraft Center Department of Aerospace Engineering To study the Dynamic Stalling of rotor blade cross-sections Unsteady Aerodynamics: Time varying
More informationATM 298, Spring 2013 Lecture 4 Numerical Methods: Horizontal DiscreDzaDons April 10, Paul A. Ullrich (HH 251)
ATM 298, Spring 2013 Lecture 4 Numerical Methods: Horizontal DiscreDzaDons April 10, 2013 Paul A. Ullrich (HH 251) paullrich@ucdavis.edu Outline 1. Introduction / Motivation 2. Finite Difference Methods
More information1 Exercise: Heat equation in 2-D with FE
1 Exercise: Heat equation in 2-D with FE Reading Hughes (2000, sec. 2.3-2.6 Dabrowski et al. (2008, sec. 1-3, 4.1.1, 4.1.3, 4.2.1 This FE exercise and most of the following ones are based on the MILAMIN
More informationMöbius Transformations in Scientific Computing. David Eppstein
Möbius Transformations in Scientific Computing David Eppstein Univ. of California, Irvine School of Information and Computer Science (including joint work with Marshall Bern from WADS 01 and SODA 03) Outline
More informationRobust Numerical Methods for Singularly Perturbed Differential Equations SPIN Springer s internal project number, if known
Hans-Görg Roos Martin Stynes Lutz Tobiska Robust Numerical Methods for Singularly Perturbed Differential Equations SPIN Springer s internal project number, if known Convection-Diffusion-Reaction and Flow
More informationDriven Cavity Example
BMAppendixI.qxd 11/14/12 6:55 PM Page I-1 I CFD Driven Cavity Example I.1 Problem One of the classic benchmarks in CFD is the driven cavity problem. Consider steady, incompressible, viscous flow in a square
More informationChapter 13. Boundary Value Problems for Partial Differential Equations* Linz 2002/ page
Chapter 13 Boundary Value Problems for Partial Differential Equations* E lliptic equations constitute the third category of partial differential equations. As a prototype, we take the Poisson equation
More informationSolving Partial Differential Equations on Overlapping Grids
**FULL TITLE** ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Solving Partial Differential Equations on Overlapping Grids William D. Henshaw Centre for Applied Scientific
More informationBASICS OF FLUID MECHANICS AND INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS
BASICS OF FLUID MECHANICS AND INTRODUCTION TO COMPUTATIONAL FLUID DYNAMICS Numerical Methods and Algorithms Volume 3 Series Editor: Claude Brezinski Université des Sciences et Technologies de Lille, France
More information2.7 Cloth Animation. Jacobs University Visualization and Computer Graphics Lab : Advanced Graphics - Chapter 2 123
2.7 Cloth Animation 320491: Advanced Graphics - Chapter 2 123 Example: Cloth draping Image Michael Kass 320491: Advanced Graphics - Chapter 2 124 Cloth using mass-spring model Network of masses and springs
More informationA Random Variable Shape Parameter Strategy for Radial Basis Function Approximation Methods
A Random Variable Shape Parameter Strategy for Radial Basis Function Approximation Methods Scott A. Sarra, Derek Sturgill Marshall University, Department of Mathematics, One John Marshall Drive, Huntington
More informationOverview of Traditional Surface Tracking Methods
Liquid Simulation With Mesh-Based Surface Tracking Overview of Traditional Surface Tracking Methods Matthias Müller Introduction Research lead of NVIDIA PhysX team PhysX GPU acc. Game physics engine www.nvidia.com\physx
More informationDevelopment of a Maxwell Equation Solver for Application to Two Fluid Plasma Models. C. Aberle, A. Hakim, and U. Shumlak
Development of a Maxwell Equation Solver for Application to Two Fluid Plasma Models C. Aberle, A. Hakim, and U. Shumlak Aerospace and Astronautics University of Washington, Seattle American Physical Society
More informationCME 345: MODEL REDUCTION
CME 345: MODEL REDUCTION Parameterized Partial Differential Equations Charbel Farhat Stanford University cfarhat@stanford.edu 1 / 19 Outline 1 Initial Boundary Value Problems 2 Typical Parameters of Interest
More informationLevel Set Method in a Finite Element Setting
Level Set Method in a Finite Element Setting John Shopple University of California, San Diego November 6, 2007 Outline 1 Level Set Method 2 Solute-Solvent Model 3 Reinitialization 4 Conclusion Types of
More informationAdaptive-Mesh-Refinement Pattern
Adaptive-Mesh-Refinement Pattern I. Problem Data-parallelism is exposed on a geometric mesh structure (either irregular or regular), where each point iteratively communicates with nearby neighboring points
More informationCloth Simulation. COMP 768 Presentation Zhen Wei
Cloth Simulation COMP 768 Presentation Zhen Wei Outline Motivation and Application Cloth Simulation Methods Physically-based Cloth Simulation Overview Development References 2 Motivation Movies Games VR
More informationOverview. Applications of DEC: Fluid Mechanics and Meshing. Fluid Models (I) Part I. Computational Fluids with DEC. Fluid Models (II) Fluid Models (I)
Applications of DEC: Fluid Mechanics and Meshing Mathieu Desbrun Applied Geometry Lab Overview Putting DEC to good use Fluids, fluids, fluids geometric interpretation of classical models discrete geometric
More informationIMPROVED WALL BOUNDARY CONDITIONS WITH IMPLICITLY DEFINED WALLS FOR PARTICLE BASED FLUID SIMULATION
6th European Conference on Computational Mechanics (ECCM 6) 7th European Conference on Computational Fluid Dynamics (ECFD 7) 1115 June 2018, Glasgow, UK IMPROVED WALL BOUNDARY CONDITIONS WITH IMPLICITLY
More informationImagery for 3D geometry design: application to fluid flows.
Imagery for 3D geometry design: application to fluid flows. C. Galusinski, C. Nguyen IMATH, Université du Sud Toulon Var, Supported by ANR Carpeinter May 14, 2010 Toolbox Ginzburg-Landau. Skeleton 3D extension
More informationFinite Volume Discretization on Irregular Voronoi Grids
Finite Volume Discretization on Irregular Voronoi Grids C.Huettig 1, W. Moore 1 1 Hampton University / National Institute of Aerospace Folie 1 The earth and its terrestrial neighbors NASA Colin Rose, Dorling
More informationAvailable online at ScienceDirect. Parallel Computational Fluid Dynamics Conference (ParCFD2013)
Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 61 ( 2013 ) 81 86 Parallel Computational Fluid Dynamics Conference (ParCFD2013) An OpenCL-based parallel CFD code for simulations
More informationCS 231. Fluid simulation
CS 231 Fluid simulation Why Simulate Fluids? Feature film special effects Computer games Medicine (e.g. blood flow in heart) Because it s fun Fluid Simulation Called Computational Fluid Dynamics (CFD)
More informationMath 690N - Final Report
Math 690N - Final Report Yuanhong Li May 05, 008 Accurate tracking of a discontinuous, thin and evolving turbulent flame front has been a challenging subject in modelling a premixed turbulent combustion.
More informationACCELERATING CFD AND RESERVOIR SIMULATIONS WITH ALGEBRAIC MULTI GRID Chris Gottbrath, Nov 2016
ACCELERATING CFD AND RESERVOIR SIMULATIONS WITH ALGEBRAIC MULTI GRID Chris Gottbrath, Nov 2016 Challenges What is Algebraic Multi-Grid (AMG)? AGENDA Why use AMG? When to use AMG? NVIDIA AmgX Results 2
More informationHigh Order Nédélec Elements with local complete sequence properties
High Order Nédélec Elements with local complete sequence properties Joachim Schöberl and Sabine Zaglmayr Institute for Computational Mathematics, Johannes Kepler University Linz, Austria E-mail: {js,sz}@jku.at
More information