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

作　　者：Laiping Zhang Ming Li Wei Liu Xin He 

机构地区：[1]State Key Laboratory of Aerodynamics,Mianyang,Sichuan,621000,China [2]China Aerodynamics Research and Development Center,Mianyang,Sichuan,621000,China

出　　处：《Communications in Computational Physics》2015年第1期287-316,共30页计算物理通讯（英文）

基　　金：This work is supported partially by National Basic Research Program of China(Grant No.2009CB723800);by National Science Foundation of China(Grant Nos.11402290 and 91130029).

摘　　要：A Newton/LU-SGS(lower-upper symmetric Gauss-Seidel)iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids.The Newton iteration was employed to 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 investigated 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 channel was simulated and the effect of parameters was investigated also.Finally,the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity.The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently.Choosing 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.

关 键 词：Implicit algorithm discontinuous Galerkin method DG/FV hybrid Scheme Newton iteration Gauss-Seidel iteration 

分 类 号：O17[理学—数学]