Solving the Compressible two dimensional NAvier-Stokes Equation using Fourth order Runge-Kutta method
Author(s): Heinz-Otto Kreiss, Jens Lorenz
Series: Classics in Applied Mathematics
Publisher: SIAM: Society for Industrial and Applied Mathematics
Year: 2004
Language: English
Pages: 418
Initial-Boundary Value Problems and the Navier-Stokes Equations......Page 2
ISBN 0-89871-565-2......Page 7
Contents......Page 8
Preface to the Classics Edition......Page 12
Errata......Page 14
Introduction......Page 16
1 The Navier-Stokes Equations......Page 20
2 Constant-Coefficient Cauchy Problems......Page 42
3 Linear Variable-Coefficient Cauchy Problems in ID......Page 100
4 A Nonlinear Example: Burgers' Equation......Page 140
5 Nonlinear Systems in One Space Dimension......Page 177
6 The Cauchy Problem for Systems in Several Dimensions......Page 194
7 Initial-Boundary Value Problems in One Space Dimension......Page 220
8 Initial-Boundary Value Problems in Serveral Space Dimension......Page 292
9 The Incompressible Navier-Stokes Equations: The Spatially Periodic Case......Page 342
10 The Incompressible Navier-Stokes Equations under Initial and Boundary Conditions......Page 362
Appendix 1 Notations and Results from Linear Algebra......Page 377
Appendix 2 Interpolation......Page 381
Appendix 3 Sobolev Inequalities......Page 387
Appendix 4 Application of the Arzela-Ascoli Theorem......Page 405
References......Page 409
Author Index......Page 415
Subject Index......Page 417
