Parameter investigation with line-implicit lower–upper symmetric Gauss–Seidel on 3D stretched grids

Abstract

An implicit lower–upper symmetric Gauss–Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier–Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier–Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGSsolver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant–Friedrichs–Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANScomputations for comparison with explicit and line-implicit Runge–Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.