Data-Parallel Right-Updating Algorithm for the Discontinuous Galerkin Method in Compressible Viscous Flow

A new implicit method has been developed based on the full matrix data-parallel lower-upper relaxation (DP-LUR) method. This method maintains data independence between cells and decreases memory usage in subiterations through repeated right side updating. Two schemes have been implemented for this application. The first scheme is a variant of the DP-LUR method. Enhanced with an lower-upper symmetric Gauss-Seidel preconditioner, the second scheme aims to reduce the residual oscillations observed in the first scheme. Numerical tests, encompassing both laminar and turbulent flows, have been conducted. The results demonstrate that both schemes achieve desirable performance with reduced memory usage and exhibit good stability at higher Courant–Friedrichs–Lewy numbers, thus accelerating convergence with appropriate settings. The first scheme achieves performance comparable to the original DP-LUR method, while the second scheme yields better results when the subiteration count is limited.