Abstract
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. A very simple overrelaxation is additionally executed in the LU-SGS method coupled with diagonal flux splitting. Then, an overrelaxation parameter w, 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
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