欧拉方程的高阶间断Galerkin方法研究

High-order discontinuous Galerkin method for solving Euler equations

在二维结构网格上建立了一种求解欧拉方程的快速稳健高阶间断Galerkin方法.采用Roe迎风型数值通量,时间步采用TVD Runge-Kutta方法推进;构造了适合间断Galerkin方法的二维二阶Moment限制器,并采用当地时间步长加速收敛.数值模拟了绕NACA0012翼型流场,数值结果表明了Moment限制器有效地抑制了数值振荡,该方法具有优良的加速收敛效果和较好地激波捕捉能力.

A fast and robust high-order discontinuous Galerkin algorithm using normal orthogonal basis functions is presented for the solution of compressible Euler equations on structured grids.The methodology is developed using both Roe upwind flux and TVD Runge-Kutta multiple method in temporal step.Moreover,this paper investigates 2D two-order Moment limiter and uses local time step technique to accelerate the convergence to a steady-state solution.The calculation results are presented for a flow over the NACA0012 airfoil,and show that the algorithm has good convergence and excellent ability to capture shocks,and Moment limiter can effectively suppress the numerical oscillations.