Comparative study of LU-ADI and LU-SGS methods for the compressible Navier-stokes equations

Abstract

The lower-upper Alternating Direction Implicit (LU-ADI) factored scheme and the lower-upper Symmetric-Gauss-Seidel (LU-SGS) method, the two recent popular thin-layer Navier-Stokes equations solvers, have been studied in a comparative manner through application to a few test flow problems. LU-ADI factorization is mainly based on the implicit flux vector splitting technique which includes the simple estimation of eigenvalue of the viscous terms. On the other hand, the LU-SGS method does not require flux splitting in the approximate Newton iteration but requires scalar diagonal inversion only. The two methods have been equally applied to simple inviscid and turbulent cascade flow problems consisting of circular arc airfoils. The computational results have been compared each other and also with the existing experimental data.