Anisotropic Cartesian grid method for steady inviscid shocked flow computation

Abstract

SUMMARYThe anisotropic Cartesian grid method, initially developed by Z.N. Wu (ICNMFD 15, 1996; CFD Review 1998, pp. 93 -113) several years ago for e ciently capturing the anisotropic nature of a viscous boundary layer, is applied here to steady shocked ow computation. A ÿnite-di erence method is proposed for treating the slip wall conditions.

Two‐dimensional anisotropic Cartesian mesh adaptation for the compressible Euler equations

“…Solution quality improvement: It is well documented that waves travelling between cells of di erent aspect ratios experience distortion [11,5] and so the algorithms in this paper are stricter than the original ones of Ham et al, in that they place greater limits on the di erences in aspect ratio between adjacent cells. Wu and Li [5] have proposed that such di erences can adversely a ect the level of numerical dissipation present, which would suggest that the numerical methods should take neighbouring cells' aspect ratios into account when determining uxes.…”

“…Wu and Li [5] have proposed that such di erences can adversely a ect the level of numerical dissipation present, which would suggest that the numerical methods should take neighbouring cells' aspect ratios into account when determining uxes. Improvement in the quality of the solution would also serve to provide a better estimate of higher-order derivatives, opening up the possibility of using them in alternate mesh reÿnement criteria.…”

“…However, anisotropic Cartesian mesh adaptation has only been used to solve transient incompressible [4] and steady compressible [5] ows.…”

A model study for the steady state error of numerical approximations of inviscid flow equations on Cartesian grid

“…Since a cell Z.-N. WU is reÿned equally in both directions independently of the geometry and the ow gradient, the resulting Cartesian grid is isotropic. There are two types of Cartesian grid method: one is the conventional isotropic Cartesian grid method [8,11] and the other is the anisotropic Cartesian grid method proposed by the present author [12,13]. Figure 2 is the anisotropic counter part of the grid for Figure 1.…”

“…This is called anisotropic Cartesian grid. It can also be divided into two based on reÿnement only in one Z.-N. WU direction (anisotropic reÿnement, see References [12,13]). More recently, a nonet Cartesian grid method [14] is proposed for which a cell can be divided into nine subcells or six subcells so that a very strong reÿnement ratio exists.…”