An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids (Communications in Computational Physics, 2018)
A Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicitmethod was developed to solve two-dimensional Euler and Navier-Stokes equationsby the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employedto solve the nonlinear system, while the linear system was solved with LU-SGS iteration.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 investigatedto evaluate the performance of convergence history. Several typical testcases 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 thepresent DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channelwas simulated and the effect of parameters was also investigated. Finally, the implicitalgorithm was applied to simulate a subsonic inviscid flow over a circular cylinderand the viscous flow in a square cavity. The numerical results demonstrated thatthe present implicit scheme can accelerate the convergence history efficiently. Choosingproper parameters would improve the efficiency of the implicit scheme. Moreover,in the same framework, the DG/FV hybrid schemes are more efficient than the sameorder DG schemes.