Page 154 - Computational Fluid Dynamics for Engineers

Numerical Methods for Model

Hyperbolic Equations

5.1 Introduction

The model equation used to describe the finite-difference methods for hyperbolic
equations is the linear convection equation, Eq. (4.2.5), written as

du du _
(5.1.1)
dt dx
with du/dx as the flux term. This equation can also be regarded as the model
equation for the one-dimensional vector form of the nonlinear Euler equations
given by Eqs. (2.2.30) and (2.2.45) with R e —> oo if c is taken to be a function
of u. For example, for one-dimensional flow with the neglect of viscous forces,
Eq. (2.2.30) can be written as

(5.1.2)
dt dx
where
Q <7l
9 = QU — Q2 (5.1.3a)
E t Q3
QU ei
2
E = QU + p = £2 (5.1.3b)
(E t+1 i)u ^3
Equation (5.1.2) can also be written in the form

dQ A,^dQ
(5.1.4)

with