Abstract
Numerical procedures for solving the system of conservation-law-equations of fluid flow are not as efficient as the numerical procedures developed for the scalar nonlinear potential equation used in inviscid transonic flow analysis. The solution of a system of equations requires more work than the solution of a scalar equation. This chapter reviews the use of implicit finite difference schemes to solve the Euler and Navier-Stokes equations in primitive variables. It discusses an approximate factorization (AF) implicit finite difference scheme for solving the Euler and Navier-Stokes equations. The chapter presents equations cast in generalized coordinates and highlights partial differential equation grid generation techniques used. In this approach, the flux vectors of the equations were differenced as whole quantities and time-accurate or time-like iterative schemes were used to solve the equations for general boundary surfaces. The chapter also reviews the ways of splitting and reducing the governing equations.
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