Implicit Discontinuous Galerkin Method for RANS Simulation Utilizing Pointwise Relaxation Algorithm (Communications in Computational Physics, 2010)
An efficient implicit procedure for the Discontinuous Galerkin (DG) methodis developed utilizing a pointwise relaxation algorithm. In the pointwise relaxation,those contributions from the degrees of freedom in own computational cell are accountedfor in the implicit matrix inversion. The resulting scheme is shown to be stablewith very large CFL numbers for both the Euler and the Navier-Stokes equations fortypical test problems. In order to achieve a faster convergence, efforts are also madeto reduce computing time of the present method by utilizing a p-multigrid schemeand also by solving a simplified matrix instead of a fully loaded dense matrix in theimplicit matrix inversion. A superior performance of the present implicit DG methodon the parallel computer using up to 128 PEs is shown in terms of readily achievablescalability and high parallel efficiency. The RANS simulation of turbulent flowfieldover AGARD-B model is carried out to show the convergence property and numericalstability of the present implicit DG method for engineering applications.