Overrelaxation applied to Lower-Upper Symmetric Gauss-Seidel Method for hypersonic flows

An implicit time-marching method for acceleration of the convergence of solution for the compressible Navier-Stokes equations is presented. This is based on the lower-upper symmetric-Gauss-Seidel (LU-SGS) method proposed by Yoon and Jameson (Yoon, S., and Jameson, A., "Lower-Upper Symmetric-Ganss- Seidel Method for the Euler and Navier-Stokes Equations," AIAA Journal, Vol. 26, 1988, pp. 1025-1026). A very simple overtaxation is additionally executed in the LU-SGS method coupled with diagonal flux splitting. Then, an overrelaxation parameter ω, a parameter similar to that in the well-known successive-overrelaxation method is introduced. The calculated results for a hypersonic viscous flows around a cylinder and through a compression corner indicate that the convergence is accelerated by a proper value of ω(1 < ω < 2). This method is also applied to a hypersonic thermochemical nonequilibrium flow around a sphere.