AN IMPLICIT ALGORITHM FOR DISCONTINUOUS GALERKIN METHOD BASED ON NEWTON/GAUSS-SEIDEL ITERATIONS

An efficient implicit algorithm was developed for high-order discontinuous Galerkin (DGM) based on Newton/Gauss-Seidel iteration approach. The second-order to the forth order DGMs based on Taylor basis functions were employed to carry out the spatial discretization. Newton iteration scheme was used to solve the nonlinear system, and the linear system was solved with one-step Gauss-Seidel iteration. In addition, the effects of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of mass-matrix, have been investigated for two-dimensional Euler equations. Two typical cases, including subsonic flows over a bump and a NACA0012 airfoil, were simulated, and compared with the traditional explicit Runge-Kutta scheme. The numerical results demonstrate that the present implicit scheme can accelerate the convergence history evidently.