曲线网格下精确四阶精度有限体积紧致方法

A Fourth-Order-Accurate and Compact Finite Volume Method(FVM) on Curvilinear Grids

研究了一种求解可压缩欧拉方程的精确四阶精度有限体积紧致方法。通过引入坐标变换,构造了精确四阶精度的体平均量近似和面平均量近似方法,以解决有限体积方法中的积分近似问题,并在曲线网格上辅助四阶精度Padé型紧致格式对欧拉方程进行空间离散。构造了积分型高精度紧致滤波方法代替人工粘性耗散,使计算过程收敛。通过计算欧拉圆柱绕流和Ringleb流动,验证了方法的正确性和有效性。

To our knowledge, it is difficult to apply the accurate and compact FVM to curvilinear grids because of the difficulty in calculating integral approximation accurately on curvilinear grids. With the coordinate transform, we derive the equations for calculating fourth-order-accurate cell-averaged variables and interface-averaged variables so as to solve the integral approximation problem in the FVM and the eurvilinear grid application problems. We use the fourth-order Pad6 compact scheme to carry out the spatial diseretization of the Euler equations. We derive an in- tegral-type high-order compact filtering equation to replace the artificial dissipation in order to converge the calcula- tion in the time marching process. Finally, we give two numerical simulation examples to verify the correctness and effectiveness of our method. The simulation results, given in Figs. 2 through 6 and Table 1, show preliminarily that ： （ 1 ） the calculation of the flow over a cylinder and the Ringleb flow with our method can reach the fourth-or- der accuracy; （2） our method can accomplish high-order integral approximation and solve the curvilinear grid ap- plication problems.