Hydrodynamics - Fundamentals of Computational Fluid Dynamics.pdf

F undamen tals putational Fluid
Dynamics
Harv ard Lomax and Thomas H
Pulliam
NASA Ames Researc h Cen ter
Da vid W
Zingg
Univ ersit y of T oron to Institute for Aerospace Studies
August
Con ten ts
INTR ODUCTION

Motiv ation

Bac kground

Problem Sp eci
cation and Geometry Preparation

Selection of Go v erning Equations and Boundary Conditions

Selection of Gridding Strategy and Numerical Metho d

Assessmen t and In terpretation of Results

Ov erview

Notation

CONSER V A TION LA WS AND THE MODEL EQUA TIONS

Conserv ation La ws

The Na vier
Stok es and Euler Equations

The Linear Con v ection Equation

Di
eren tial F orm

Solution in W a v e Space

The Di
usion Equation

Di
eren tial F orm

Solution in W a v e Space

Linear Hyp erb olic Systems

Problems

FINITE
DIFFERENCE APPR O XIMA TIONS

Meshes and Finite
Di
erence Notation

Space Deriv ativ eAppro ximations

Finite
Di
erence Op erators

P oin t Di
erence Op erators

Matrix Di
erence Op erators

P erio dic Matrices

Circulan t Matrices
iii
Constructing Di
erencing Sc hemes of An y Order

T a ylor T ables

Generalization of Di
erence F orm ulas