An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids

ANewton/LU-SGS(lower-uppersymmetric Gauss-Seidel)iterationimplicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrarygrids. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with LU-SGS itera- tion. The effect of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was in- vestigated to evaluate the performance of convergence history. Several typical test cases were simulated, and compared with the traditional explicit Runge-Kutta (RK) scheme. Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a chan- nel was simulated and the effect of parameters was investigated also. Finally, the im- plicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylin- der and the viscous flow in a square cavity. The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently. Choos- ing proper parameters would improve the efficiency of the implicit scheme. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.