文档介绍：Fundamentals putational Fluid
Dynamics
Harvard Lomax and Thomas H. Pulliam
NASA Ames Research Center
David W. Zingg
University of Toronto Institute for Aerospace Studies
August 26, 1999
Contents
1 INTRODUCTION 1
Motivation ................................. 1
Background ................................ 2
Problem Specification and Geometry Preparation . ...... 2
Selection of Governing Equations and Boundary Conditions . 3
Selection of Gridding Strategy and Numerical Method .... 3
Assessment and Interpretation of Results ............ 4
Overview .................................. 4
Notation .................................. 5
2 CONSERVATION LAWS AND THE MODEL EQUATIONS 7
Conservation Laws ............................ 7
The Navier-Stokes and Euler Equations ................. 8
The Linear Convection Equation . . . ................. 12
Differential Form ......................... 12
Solution in Wave Space ...................... 13
The Diffusion Equation .......................... 14
Differential Form ......................... 14
Solution in Wave Space ...................... 15
Linear Hyperbolic Systems ........................ 16
Problems .................................. 17
3 FINITE-DIFFERENCE APPROXIMATIONS 21
Meshes and Finite-Difference Notation ................. 21
Space Derivative Approximations . . . ................. 24
Finite-Difference Operators ....................... 25
Point Difference Operators . . . ................. 25
Matrix Difference Operators . . ................. 25
Periodic Matrices ......................... 29
Circulant Matrices ........................ 30
iii
Constructing Differencing Schemes of Any Order ............ 31
Taylor Tables ........................... 31
Generalization of Difference Formulas .............. 34
Lagrange and Hermite