Mimetic discretization methods

Front Cover......Page 1
Contents......Page 6
List of Figures......Page 10
List of Tables......Page 14
List of Algorithms......Page 16
List of Symbols......Page 18
Preface......Page 20
Acknowledgments......Page 24
1. Introduction......Page 26
2. Continuum Mathematical Models......Page 32
3. Notes on Numerical Analysis......Page 56
4. Mimetic Differential Operators......Page 68
5. Object-Oriented Programming and C++......Page 106
6. Mimetic Methods Toolkit (MTK)......Page 128
7. Nonuniform Structured Meshes......Page 146
8. Case Studies......Page 154
A. Heuristic Deduction of the Extended Form of Gauss' Divergence Theorem......Page 202
B. Tensor Concept: An Intuitive Approach......Page 208
C. Total Force Due to Pressure Gradients......Page 216
D. Heuristic Deduction of Stokes' Formula......Page 218
E. Curl in a Rotating Incompressible Inviscid Liquid......Page 222
F. Curl in Poiseuille's Flow......Page 224
G. Green's Identities......Page 226
H. Fluid Volumetric Time-Tate of Change......Page 228
I. General Formulation of the Flux Concept......Page 232
J. Fourth-Order Castillo–Grone Divergence Operators......Page 234
References......Page 242