Premium
An efficient upwind/relaxation algorithm for the Euler and Navier–Stokes equations
Author(s) -
Zha GeCheng,
Liu DaoZhi,
Ma TieYou
Publication year - 1989
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650090503
Subject(s) - mathematics , inviscid flow , euler equations , transonic , euler's formula , backward euler method , solver , mathematical analysis , finite volume method , upwind scheme , geometry , mechanics , physics , mathematical optimization , discretization , aerodynamics
An efficient Euler and full Navier–Stokes solver based on a flux splitting scheme is presented. The original Van Leer flux vector splitting form is extended to arbitrary body‐fitted co‐ordinates in the physical domain so that it can be used with a finite volume scheme. The block matrix is inverted by Gauss–Seidel iteration. It is verified that the often used reflection boundary condition will produce incorrect flux crossing the wall and cause too large numerical dissipation if flux vector splitting is used. To remove such errors, an appropriate treatment of wall boundary conditions is suggested. Inviscid and viscous steady transonic internal flows are analysed, including the case of shock‐induced boundary layer separation.