Mimetic Discretization Methods

ISBN: 9780367380434 出版年：2013 页码：256 Castillo, Jose E Miranda, Guillermo F CRC Press

Introduction Continuum Mathematical Models Physically Motivated Mathematical Concepts and Theorems General 3-D Use of Flux Vector Densities Illustrative Examples of PDEs A Comment on the Numerical Treatment of the grad Operator Notes on Numerical Analysis Computational Errors Order of Accuracy Norms and Condition Numbers Linear Systems of Equations Solution of Nonlinear Equations Mimetic Differential Operators Castillo-Grone Method for 1-D Uniform Staggered Grids Higher-Dimensional CGM 2-D Staggerings 3-D Staggerings Gradient Compositions Nullity Tests Higher-Order Operators Formulation of Nonlinear and Time-Dependent Problems Object-Oriented Programming and C++ From Structured to Object-Oriented Programming Fundamental Concepts in Object-Oriented Programming Object-Oriented Modeling and UML Inheritance and Polymorphism Mimetic Methods Toolkit (MTK) MTK Usage Philosophy Study of a Diffusive-Reactive Process Using the MTK Collaborative Development of the MTK: Flavors and Concerns Downloading the MTK Nonuniform Structured Meshes Divergence Operator Gradient Operator Case Studies Porous Media Flow and Reservoir Simulation Modeling Carbon Dioxide Geologic Sequestration Maxwell's Equations Wave Propagation Geophysical Flow Appendix A: Heuristic Deduction of the Extended Form of Gauss' Divergence Theorem Appendix B: Tensor Concept: An Intuitive Approach Appendix C Total Force Due to Pressure Gradients Appendix D: Heuristic Deduction of Stokes' Formula Appendix E: Curl in a Rotating Incompressible Inviscid Liquid Appendix F: Curl in Poiseuille's Flow Appendix G: Green's Identities Appendix H: Fluid Volumetric Time-Tate of Change Appendix I: General Formulation of the Flux Concept Appendix J: Fourth-Order Castillo-Grone Divergence Operators References Index Sample Problems appear at the end of each chapter.