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• Developing a Fuel Tank with the Help of Computer Aided Engineering (CAE).- Deriving a System of Equations for the Description of Sloshing Phenomena.- Showing the Usability of the Finite Volume Method.- Verifying the Results for Suitable Test Cases.
• (source: Nielsen Book Data)

Matthaus Jager examines the simulation of liquid-gas flow in fuel tank systems and its application to sloshing problems. The author focuses at first on the physical model and the assumptions necessary to derive the respective partial differential equations. The second step involves the cell-centered finite volume method and its application to fluid dynamic problems with free surfaces using a volume of fluid approach. Finally, the application of the method for different use cases is presented followed by an introduction to the methodology for the interpretation of the results achieved.
(source: Nielsen Book Data)

• Chapter 1 Introduction
• Chapter 2 Conservation laws of fluid motion and their boundary conditions
• Chapter 3 Turbulence and its modelling
• Chapter 4 The finite volume method for diffusion problems
• Chapter 5 The finite volume method for convection-diffusion problems
• Chapter 6 Solution algorithms for pressure-velocity coupling in steady flows
• Chapter 7 Solution of systems of discretised equations
• Chapter 8 The finite volume method for unsteady flows
• Chapter 9 Implementation of boundary conditions
• Chapter 10 Uncertainty in CFD modelling
• Chapter 11 Methods for dealing with complex geometries
• Chapter 12 CFD modelling of combustion
• Chapter 13 Numerical calculation of radiative heat transfer Appendices References Index.
• (source: Nielsen Book Data)

This established, leading textbook, is suitable for courses in CFD. The new edition covers new techniques and methods, as well as considerable expansion of the advanced topics and applications (from one to four chapters). This book presents the fundamentals of computational fluid mechanics for the novice user. It provides a thorough yet user-friendly introduction to the governing equations and boundary conditions of viscous fluid flows, turbulence and its modelling, and the finite volume method of solving flow problems on computers.
(source: Nielsen Book Data)

• *Introduction. *Conservation Laws of Fluid Motion and Boundary Conditions. *Turbulence and its Modelling. *The Finite Volume Method for Diffusion Problems. *The Finite Volume Method for Convection-Diffusion Problems. *Solution Algorithms for Pressure-Velocity Coupling in Steady Flows. *Solution of Discretised Equations. *The Finite Volume Method for Unsteady Flows. *Implementation of Boundary Conditions. *Advanced topics and applications. Appendices. References. Index.
• (source: Nielsen Book Data)

This book presents some of the fundamentals of computational fluid dynamics for the novice. It provides a thorough yet user-friendly introduction to the governing equations and boundary conditions of viscous fluid flows, turbulence and its modelling and the finite volume method of solving flow patters on a computer.
(source: Nielsen Book Data)

• 1 Introduction.- 2 Layer-adapted meshes.- Part I One dimensional problems.- 3 The analytical behaviour of solutions.- 4 Finite difference schemes for convection-diffusion problems.- 5 Finite element and finite volume methods.- 6 Discretisations of reaction-convection-diffusion problems.- Part II Two dimensional problems.- 7 The analytical behaviour of solutions.- 8 Reaction-diffusion problems.- 9 Convection-diffusion problems.
• (source: Nielsen Book Data)

• Governing Equations
• The Essential Ingredients in a Numerical Solution
• Control Volume Finite Element Data Structure
• Control Volume Finite Element Method (CVFEM) Discretization and Solution
• The Control Volume Finite Difference Method
• Analytical and CVFEM Solutions of Advection-Diffusion Equations
• The CVFEM Solution for Plane Stress and Plane Strain Elasticity
• The CVFEM Solution for the Stream-Function Vorticity Form of the Navier-Stokes Equations
• Notes for the Extension of CVFEM to Three Dimensions.
• (source: Nielsen Book Data)

The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems.
(source: Nielsen Book Data)

• Part I Invited contributions. P. Bochev: Compatible Discretizations for Partial Differential Equations.- F. Bouchu: Finite Volume Methods for Shallow Water Equations, Hyperbolic Equations, Magnetohydrodynamics.- C. Chainais-Hillairet: Finite Volume Methods for Drift-Diffusion Equations.- M. Dumbser: High Order One-Step AMR and ALE Methods for Hyperbolic PDE.- P. Helluy: Compressible Multiphase Flows.- K. Mikula: Finite Volumes in Image Processing and Groundwater Flow.- S. Mishra: Finite Volume Methods for Conservation Laws, Uncertainty Quantification.- Part II Theoretical aspects of Finite Volume Methods.
• (source: Nielsen Book Data)

The first volume of the proceedings of the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) covers topics that include convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers, as well as the reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods. Altogether, a rather comprehensive overview is given of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.
(source: Nielsen Book Data)

• PART 4. Hyperbolic Problems. David Iampietro, Frederic Daude, Pascal Galon, and Jean-Marc Herard, A Weighted Splitting Approach For Low-Mach Number Flows.- Florence Hubert and Remi Tesson, Weno scheme for transport equation on unstructured grids with a DDFV approach.- M.J. Castro, J.M. Gallardo and A. Marquina, New types of Jacobian-free approximate Riemann solvers for hyperbolic systems.- Charles Demay, Christian Bourdarias, Benoit de Laage de Meux, Stephane Gerbi and Jean-Marc Herard, A fractional step method to simulate mixed flows in pipes with a compressible two-layer model.- Theo Corot, A second order cell-centered scheme for Lagrangian hydrodynamics.- Clement Colas, Martin Ferrand, Jean-Marc Herard, Erwan Le Coupanec and Xavier Martin, An implicit integral formulation for the modeling of inviscid fluid flows in domains containing obstacles.- Christophe Chalons and Maxime Stauffert, A high-order Discontinuous Galerkin Lagrange Projection scheme for the barotropic Euler equations.- Christophe Chalons, Regis Duvigneau and Camilla Fiorini, Sensitivity analysis for the Euler equations in Lagrangian coordinates.- Jooyoung Hahn, Karol Mikula, Peter Frolkovic, and Branislav Basara, Semi-implicit level set method with inflow-based gradient in a polyhedron mesh.- Thierry Goudon, Julie Llobell and Sebastian Minjeaud, A staggered scheme for the Euler equations.- Christian Bourdarias, Stephane Gerbi and Ralph Lteif, A numerical scheme for the propagation of internal waves in an oceanographic model.- Hamza Boukili and Jean-Marc Herard, A splitting scheme for three-phase flow models.- M. J Castro, C. Escalante and T. Morales de Luna, Modelling and simulation of non-hydrostatic shallow flows.- Svetlana Tokareva and Eleuterio Toro, A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow.- Mohamed Boubekeur and Fayssal Benkhaldoun and Mohammed Seaid, GPU accelerated finite volume methods for three-dimensional shallow water flows.- Ward Melis, Thomas Rey and Giovanni Samaey, Projective integration for nonlinear BGK kinetic equations.- Lei Zhang, Jean-Michel Ghidaglia and Anela Kumbaro, Asymptotic preserving property of a semi-implicit method.- Sebastien Boyaval, A Finite-Volume discretization of viscoelastic Saint-Venant equations for FENE-P fluids.- David Coulette, Emmanuel Franck, Philippe Helluy, Michel Mehrenberger, Laurent Navoret, Palindromic Discontinuous Galerkin Method.- M. Lukacova-Medvid'ova, J. Rosemeier, P. Spichtinger and B. Wiebe, IMEX finite volume methods for cloud simulation.- Raimund Burger and Ilja Kroker, Hybrid stochastic Galerkin finite volumes for the diffusively corrected Lighthill-Whitham-Richards traffic model.- Hamed Zakerzadeh, The RS-IMEX scheme for the rotating shallow water equations with the Coriolis force.- Emmanuel Audusse, Minh Hieu Do, Pascal Omnes, Yohan Penel, Analysis of Apparent Topography scheme for the linear wave equation with Coriolis force.- N. Aissiouene, M-O. Bristeau, E. Godlewski, A. Mangeney, C. Pares and J. Sainte-Marie, Application of a combined finite element - finite volume method to a 2D non-hydrostatic shallow water problem.- Emanuela Abbate, Angelo Iollo and Gabriella Puppo, A relaxation scheme for the simulation of low Mach number flows.- Stefan Vater, Nicole Beisiegel and Jorn Behrens, Comparison of wetting and drying between a RKDG2 method and classical FV based second-order hydrostatic reconstruction.- Anja Jeschke, Stefan Vater and Jorn Behrens, A Discontinuous Galerkin Method for Non-Hydrostatic Shallow Water Flows.- Remi Abgrall and Paola Bacigaluppi, Design of a Second-Order Fully Explicit Residual Distribution Scheme for Compressible Multiphase Flows.- Martin Campos Pinto, An Unstructured Forward-Backward Lagrangian Scheme for Transport Problems.- Nicole Goutal, Minh-Hoang Le and Philippe Ung, A Godunov-type scheme for Shallow Water equations dedicated to simulations of overland flows on stepped slopes.- Dionysios Grapsas, Raphaele Herbin and Jean-Claude Latche, Two models for the computation of laminar flames in dust clouds.- Gregoire Pont, Pierre Brenner, High order finite volume scheme and conservative grid overlapping technique for complex industrial applications.-
• PART 5. Elliptic and Parabolic problems. Sarvesh Kumar, Ricardo Ruiz-Baier, Ruchi Sandilya, Discontinuous finite volume element methods for the optimal control of Brinkman equations.- L. Beaude, K. Brenner, S. Lopez, R. Masson, F. Smai, Non-isothermal compositional two-phase Darcy flow: formulation and outflow boundary condition.- Clement Cances, Didier Granjeon, Nicolas Peton, Quang Huy Tran, and Sylvie Wolf, Numerical scheme for a stratigraphic model with erosion constraint and nonlinear gravity flux.- Christoph Erath and Robert Schorr, Comparison of adaptive non-symmetric and three-field FVM-BEM coupling.- Thomas Fetzer, Christoph Gruninger, Bernd Flemisch, Rainer Helmig, On the Conditions for Coupling Free Flow and Porous-Medium Flow in a Finite Volume Framework.- Mario Ohlberger and Felix Schindler, Non-Conforming Localized Model Reduction with Online Enrichment: Towards Optimal Complexity in PDE constrained Optimization.- Hanz Martin Cheng and Jerome Droniou, Combining the Hybrid Mimetic Mixed method and the Eulerian Lagrangian Localised Adjoint Method for approximating miscible flows in porous media.- Ambartsumyan, E. Khattatov and I. Yotov, Mixed finite volume methods for linear elasticity.- Nabil Birgle, Roland Masson and Laurent Trenty, A nonlinear domain decomposition method to couple compositional gas liquid Darcy and free gas flows.- Jurgen Fuhrmann, Annegret Glitzky and Matthias Liero, Hybrid Finite-Volume/Finite-Element Schemes for p(x)-Laplace Thermistor Models.- E. Ahusborde, B. Amaziane and M. El Ossmani, Finite Volume Scheme for Coupling Two-Phase Flow with Reactive Transport in Porous Media.- Martin Schneider, Dennis Glaser, Bernd Flemisch and Rainer Helmig, Nonlinear finite-volume scheme for complex flow processes on corner-point grids.- Daniil Svyatskiy and Konstantin Lipnikov, Consistent nonlinear solver for solute transport in variably saturated porous media.- Jan ten Thije Boonkkamp, Martijn Anthonissen and Ruben Kwant, A two-dimensional complete flux scheme in local flow adapted coordinates.- Birane Kane, Robert Klofkorn, Christoph Gersbacher, hp-Adaptive Discontinuous Galerkin Methods for Porous Media Flow.- N. Kumar, J.H.M. ten Thije Boonkkamp, B. Koren and A. Linke, A Nonlinear Flux Approximation Scheme for the Viscous Burgers Equation.- Rene Beltman, Martijn Anthonissen and Barry Koren, Mimetic Staggered Discretization of Incompressible Navier-Stokes for Barycentric Dual Mesh.- Sebastien Boyaval, Guillaume Enchery, Riad Sanchez and Quang Huy Tran, A reduced-basis approach to two-phase flow in porous media.- Sebastien Boyaval, Guillaume Enchery, Riad Sanchez and Quang Huy Tran, On the capillary pressure in basin modeling.- Jurgen Fuhrmann, Clemens Guhlke, A finite volume scheme for Nernst-Planck-Poisson systems with ion size and solvation effects.- Vasiliy Kramarenko, Kirill Nikitin, and Yuri Vassilevski, A nonlinear correction FV scheme for near-well regions.- Florent Chave, Daniele A. Di Pietro and Fabien Marche, A Hybrid High-Order method for the convective Cahn-Hilliard problem in mixed form.- Alexey Chernyshenko, Maxim Olshahskii and Yuri Vassilevski, A hybrid finite volume - finite element method for modeling flows in fractured media.- Michele Botti, Daniele A. Di Pietro, and Pierre Sochala, A nonconforming high-order method for nonlinear poroelasticity.- Hanen Amor and Fayssal Benkhaldoun and Tarek Ghoudi and Imad Kissami and Mohammed Seaid, New criteria for mesh adaptation in finite volume simulation of planar ionization wave front propagation.- Author Index.
• (source: Nielsen Book Data)

This book is the second volume of proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017). It includes reviewed contributions reporting successful applications in the fields of fluid dynamics, computational geosciences, structural analysis, nuclear physics, semiconductor theory and other topics. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete l evel. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is useful for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as for engineers working in numerical modeling and simulations.
(source: Nielsen Book Data)

• PART 1. Invited Papers. Chi-Wang Shu, Bound-preserving high order finite volume schemes for conservation laws and convection-diffusion equations.-E.D. Fernandez-Nieto, Some geophysical applications with finite volume solvers of two-layer and two-phase systems.-Thierry Gallouet, Some discrete functional analysis tools.-Yuanzhen Cheng, Alina Chertock and Alexander Kurganov, A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles.-
• PART 2. Franck Boyer and Pascal Omnes, Benchmark on discretization methods for viscous incompressible flows. Benchmark proposal for the FVCA8 conference : Finite Volume methods for the Stokes and Navier-Stokes equations.-Louis Vittoz, Guillaume Oger, Zhe Li, Matthieu De Leffe and David Le Touze, A high-order Finite Volume solver on locally refined Cartesian meshes.-Daniele A. Di Pietro and Stella Krell, Benchmark session : The 2D Hybrid High-Order method.-Jerome Droniou and Robert Eymard, Benchmark: two Hybrid Mimetic Mixed schemes for the lid-driven cavity.-Eric Chenier, Robert Eymard and Raphaele Herbin, Results with a locally refined MAC scheme - benchmark session.-Sarah Delcourte and Pascal Omnes, Numerical results for a discrete duality finite volume discretization applied to the Navier-Stokes equations.-Franck Boyer and Stella Krell and Flore Nabet, Benchmark session : The 2D Discrete Duality Finite Volume Method.-P.-E. Angeli, M.-A. Puscas, G. Fauchet and A. Cartalade, FVCA8 benchmark for the Stokes and Navier-Stokes equations with the TrioCFD code - benchmark session.-
• PART 3. Theoretical Aspects of Finite Volumes. Francoise Foucher, Moustafa Ibrahim and Mazen Saad, Analysis of a Positive CVFE Scheme For Simulating Breast Cancer Development, Local Treatment and Recurrence.-Christoph Erath and Dirk Praetorius, Cea-type quasi-optimality and convergence rates for (adaptive) vertexcentered FVM.-Helene Mathis and Nicolas Therme, Numerical convergence for a diffusive limit of the Goldstein-Taylor system on bounded domain.-Florian De Vuyst, Lagrange-Flux schemes and the entropy property.-Caterina Calgaro and Meriem Ezzoug, $L^\infty$-stability of IMEX-BDF2 finite volume scheme for convection diffusion equation.-Raphaele Herbin, Jean-Claude Latche and Khaled Saleh, Low Mach number limit of a pressure correction MAC scheme for compressible barotropic flows.-T. Gallouet, R. Herbin, J.-C. Latche and K. Mallem, Convergence of the MAC scheme for variable density flows.-J. Droniou, J. Hennicker, R. Masson, Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model.-Claire Chainais-Hillairet, Benoit Merlet and Antoine Zurek, Design and analysis of a finite volume scheme for a concrete carbonation model.-Rita Riedlbeck, Daniele A. Di Pietro, and Alexandre Ern, Equilibrated stress reconstructions for linear elasticity problems with application to a posteriori error analysis.-Patricio Farrell and Alexander Linke, Uniform Second Order Convergence of a Complete Flux Scheme on Nonuniform 1D Grids.-J. Droniou and R. Eymard, The asymmetric gradient discretisation method.-Robert Eymard and Cindy Guichard, DGM, an item of GDM.-Claire Chainais-Hillairet, Benoit Merlet and Alexis F. Vasseur, Positive lower bound for the numerical solution of a convection-diffusion equation.-Francois Dubois, Isabelle Greff and Charles Pierre, Raviart Thomas Petrov Galerkin Finite Elements.-Naveed Ahmed, Alexander Linke, and Christian Merdon, Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations.-Thierry Goudon, Stella Krell and Giulia Lissoni, Numerical analysis of the DDFV method for the Stokes problem with mixed Neumann/Dirichlet boundary conditions.-J. Droniou, R. Eymard, T. Gallouet, C. Guichard and R. Herbin, An error estimate for the approximation of linear parabolic equations by the Gradient Discretization Method.-M. Bessemoulin-Chatard, C. Chainais-Hillairet, and A. Jungel, Uniform $L^\infty$ estimates for approximate solutions of the bipolar driftdiffusion system.-Abdallah Bradji, Some convergence results of a multi-dimensional finite volume scheme for a time-fractional diffusion-wave equation.-Nina Aguillon and Franck Boyer, Optimal order of convergence for the upwind scheme for the linear advection on a bounded domain.-Matus Tibensky, Angela Handlovicova, Numerical scheme for regularised Riemannian mean curvature flow equation.-Ahmed Ait Hammou Oulhaj, A finite volume scheme for a seawater intrusion model.-Clement Cances and Flore Nabet, Finite volume approximation of a degenerate immiscible two-phase flow model of Cahn-Hilliard type.-Clement Cances, Claire Chainais-Hillairet and Stella Krell, A nonlinear Discrete Duality Finite Volume Scheme for convection-diffusion equations.-Wasilij Barsukow, Stationarity and vorticity preservation for the linearized Euler equations in multiple spatial dimensions.-Jan Giesselmann and Tristan Pryer, Goal-oriented error analysis of a DG scheme for a second gradient elastodynamics model.-Alain Prignet, Simplified model for the clarinet and numerical schemes.- Author Index.
• (source: Nielsen Book Data)

This first volume of the proceedings of the 8th conference on "Finite Volumes for Complex Applications" (Lille, June 2017) covers various topics including convergence and stability analysis, as well as investigations of these methods from the point of view of compatibility with physical principles. It collects together the focused invited papers comparing advanced numerical methods for Stokes and Navier-Stokes equations on a benchmark, as well as reviewed contributions from internationally leading researchers in the field of analysis of finite volume and related methods, offering a comprehensive overview of the state of the art in the field. The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation, and recent decades have brought significant advances in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asy mptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications. The book is a valuable resource for researchers, PhD and master's level students in numerical analysis, scientific computing and related fields such as partial differential equations, as well as engineers working in numerical modeling and simulations.
(source: Nielsen Book Data)

• Governing Equations
• The Essential Ingredients in a Numerical Solution
• Control Volume Finite Element Data Structure
• Control Volume Finite Element Method (CVFEM) Discretization and Solution
• The Control Volume Finite Difference Method
• Analytical and CVFEM Solutions of Advection-Diffusion Equations
• The CVFEM Solution for Plane Stress and Plane Strain Elasticity
• The CVFEM Solution for the Stream-Function Vorticity Form of the Navier-Stokes Equations
• Notes for the Extension of CVFEM to Three Dimensions.
• (source: Nielsen Book Data)

The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems.
(source: Nielsen Book Data)

• Front Cover; Moving Particle Semi-Implicit Method; Copyright Page; Contents; Preface; 1 Introduction; 1.1 Concept of Particle Methods; 1.1.1 Lagrangian Description; 1.1.2 Meshless Discretization; 1.1.3 Continuum Mechanics; 1.2 MPS Method; 1.2.1 Weighted Difference; 1.2.2 Particle Interaction Models; 1.2.3 Semi-implicit Algorithm; 1.2.4 MPS and SPH; 1.3 Research History of Particle Methods; References; 2 Fundamentals of Fluid Simulation by the MPS Method; 2.1 The Elements of the MPS Method; 2.1.1 Setting the Initial Positions of Particles; 2.1.2 Setting Initial Velocities of Particles.

• 2.1.3 How to Move Particles2.1.4 How to Calculate Acceleration of Particles; 2.2 Basic Theory of the MPS Method; 2.2.1 Mass of a Particle; 2.2.2 Governing Equations; 2.2.2.1 The Navier-Stokes Equations; 2.2.2.1.1 Meaning of the Pressure Gradient Term; 2.2.2.1.2 Meaning of the Viscous Term; 2.2.2.2 Equation of Continuity; 2.2.2.3 Notation by Vectors; 2.2.3 Particle Number Density and Weight Function; 2.2.3.1 The Standard Particle Number Density n0; 2.2.3.2 Relationship Between Particle Number Density and Fluid Density; 2.2.3.3 Example of Calculation; 2.2.3.4 The Form of a Weight Function.

• 2.2.4 Approximation of Partial Differential Operators2.2.4.1 Gradient; 2.2.4.2 The Gradient Model of the MPS Method (Nabla Model); 2.2.4.3 The Meaning of Each Parts of the Gradient Model; 2.2.4.4 Example of Gradient Calculation; 2.2.4.5 Laplacian Operator and Its Uses; 2.2.4.6 The Laplacian Model of the MPS Method; 2.2.4.6.1 The Meaning of the Laplacian Model; 2.2.4.6.2 Example of Laplacian Calculation; 2.2.5 Semi-implicit Method; 2.2.5.1 How to Calculate Pressure, and the Necessity of the Semi-implicit Method; 2.2.5.2 Outline of the Semi-implicit Method in the MPS Method.

• 2.2.5.3 Details of the Semi-implicit Method of the MPS Method2.2.5.4 Derivation of Pressure Poison Equation of the MPS Method; 2.2.5.5 How to Calculate the Pressure Poisson Equation; 2.2.5.6 The Boundary Condition of Pressure; 2.2.5.7 The Boundary Condition of Velocity; 2.3 Outline of Simulation Programs; 2.3.1 Contents of Program; 2.3.2 How to Compile and Execute the Sample Programs; 2.3.3 How to Visualize the Simulation Result; 2.3.4 Functions of the Program; 2.3.4.1 Libraries and Declarations; 2.3.4.2 Main Function; 2.3.4.3 initializeParticlePositionAndVelocity_for 2dim() Function.

• 2.3.4.4 calculateNZeroAndLambda() Function2.3.4.5 weight() Function; 2.3.4.6 mainLoopOfSimulation() Function; 2.3.4.7 calculateGravity Function; 2.3.4.8 calculateViscosity Function; 2.3.4.9 moveParticle() Function; 2.3.4.10 calculatePressure() Function; 2.3.4.11 calculateNumberDensity() Function; 2.3.4.12 setBoundaryCondition() Function; 2.3.4.13 setSourceTerm() Function; 2.3.4.14 setMatrix() Function; 2.3.4.15 solveSimultaniousEquationsByGaussianElimination() Function; 2.3.4.16 calculatePressureGradient() Function; 2.3.4.17 calculatePressure_forExplicitMPS() Function.

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses. * Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry* Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes* Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives.
(source: Nielsen Book Data)

• Preface
• 1. Introduction
• 2. Conservation laws and differential equations
• 3. Characteristics and Riemann problems for linear hyperbolic equations
• 4. Finite-volume methods
• 5. Introduction to the CLAWPACK software
• 6. High resolution methods
• 7. Boundary conditions and ghost cells
• 8. Convergence, accuracy, and stability
• 9. Variable-coefficient linear equations
• 10. Other approaches to high resolution
• 11. Nonlinear scalar conservation laws
• 12. Finite-volume methods for nonlinear scalar conservation laws
• 13. Nonlinear systems of conservation laws
• 14. Gas dynamics and the Euler equations
• 15. Finite-volume methods for nonlinear systems
• 16. Some nonclassical hyperbolic problems
• 17. Source terms and balance laws
• 18. Multidimensional hyperbolic problems
• 19. Multidimensional numerical methods
• 20. Multidimensional scalar equations
• 21. Multidimensional systems
• 22. Elastic waves
• 23. Finite-volume methods on quadrilateral grids
• Bibliography
• Index.
• (source: Nielsen Book Data)

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
(source: Nielsen Book Data)

• Preface
• 1. Introduction
• 2. Conservation laws and differential equations
• 3. Characteristics and Riemann problems for linear hyperbolic equations
• 4. Finite-volume methods
• 5. Introduction to the CLAWPACK software
• 6. High resolution methods
• 7. Boundary conditions and ghost cells
• 8. Convergence, accuracy, and stability
• 9. Variable-coefficient linear equations
• 10. Other approaches to high resolution
• 11. Nonlinear scalar conservation laws
• 12. Finite-volume methods for nonlinear scalar conservation laws
• 13. Nonlinear systems of conservation laws
• 14. Gas dynamics and the Euler equations
• 15. Finite-volume methods for nonlinear systems
• 16. Some nonclassical hyperbolic problems
• 17. Source terms and balance laws
• 18. Multidimensional hyperbolic problems
• 19. Multidimensional numerical methods
• 20. Multidimensional scalar equations
• 21. Multidimensional systems
• 22. Elastic waves
• 23. Finite-volume methods on quadrilateral grids
• Bibliography
• Index.
• (source: Nielsen Book Data)

This book, first published in 2002, contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and engineering discipline. Several applications are described in a self-contained manner, along with much of the mathematical theory of hyperbolic problems. High-resolution versions of Godunov's method are developed, in which Riemann problems are solved to determine the local wave structure and limiters are then applied to eliminate numerical oscillations. These methods were originally designed to capture shock waves accurately, but are also useful tools for studying linear wave-propagation problems, particularly in heterogenous material. The methods studied are implemented in the CLAWPACK software package and source code for all the examples presented can be found on the web, along with animations of many of the simulations. This provides an excellent learning environment for understanding wave propagation phenomena and finite volume methods.
(source: Nielsen Book Data)

• Finite Volumes for Complex Application VI Problems & Perspectives; Editors Preface; Organization; Contents; Part I Regular Papers; Part II Invited Papers; Part III Benchmark Papers

Finite volume methods are used for various applications in fluid dynamics, magnetohydrodynamics, structural analysis or nuclear physics. A closer look reveals many interesting phenomena and mathematical or numerical difficulties, such as true error analysis and adaptivity, modelling of multi-phase phenomena or fitting problems, stiff terms in convection/diffusion equations and sources. To overcome existing problems and to find solution methods for future applications requires many efforts and always new developments. The goal of The International Symposium on Finite Volumes for Complex Applications¡VI is to bring together mathematicians, physicists and engineers dealing with Finite Volume Techniques in a wide context. This book, divided in two volumes, brings a critical look at the subject (new ideas, limits or drawbacks of methods, theoretical as well as applied topics).