Investigation on Implicit Discontinuous Galerkin Method in Unsteady Flow

An implicit discontinuous Galerkin method (DG) was investigated in order to increase the solving efficiency of unsteady flow. A second-order backward difference formulation (BDF2) was applied for the time-discretization. The Newton-Raphson method and block symmetric Gauss-Seidel (SGS) iteration were considered to solve non-linear equations and linear equations respectively. The isentropic flow around the cylinder and the Karmann vortex street phenomenon were simulated to verify the validity of the implicit DG method developed in the paper. The results show that the calculation accuracy of the implicit DG method can match designed accuracy. The solution using the implicit DG method keeps stable even the time step adopted is more than 100 times of that it has in the explicit method, with the favorable solving efficiency achieved, and the corresponding results are in good agreement with the explicit method and related references.