基于AUSM分裂的二维通量分裂格式

A 2D Flux Splitting Scheme Based on the AUSM Splitting

基于对流迎风分裂思想构造的AUSM类格式具有简单、高效、分辨率高等优点,在计算流体力学中得到了广泛的应用.传统的AUSM类格式在计算界面数值通量时只考虑网格界面法向的波系,忽略了网格界面横向波系的影响.使用Liou⁃Steffen通量分裂方法将二维Euler方程的通量分裂成对流通量和压力通量,采用AUSM格式来分别计算对流数值通量和压力数值通量.通过求解考虑了横向波系影响的角点数值通量来构造一种真正二维的AUSM通量分裂格式.在计算一维算例时,该格式保留了精确捕捉激波和接触间断的优点.在计算二维算例时,该格式不仅具有更高的分辨率而且表现出更好的鲁棒性,可以消除强激波波后的不稳定现象.此外,在多维问题的数值模拟中,该格式大大地提高了稳定性CFL数,具有更高的计算效率.因此,它是一种精确、高效并且强鲁棒性的数值方法.

The AUSM⁃type schemes based on the advection upstream splitting method have the advantages of simpleness,high efficiency and high resolution,and are widely applied in compu⁃tational fluid dynamics.The traditional AUSM⁃type schemes only consider the normal waves to the cell interface while ignoring the influence of tangential waves to the interface in the compu⁃tation of the interfacial numerical flux.The flux of 2D Euler equations was split into the convec⁃tive flux and the pressure flux by means of the AUSM splitting method,and they were both computed with the modified AUSM scheme.In the solution of the numerical flux at the corners where the influence of tangential waves was considered,a genuinely 2D AUSM flux splitting scheme was constructed.In the computation of 1D numerical examples,the proposed scheme keeps the merits of capturing shocks and contact discontinuities accurately.In the computation of the 2D numerical examples,the scheme has higher resolution and better robustness,while e⁃liminating the instability behind the strong shock waves.In addition,with the scheme the stable CFL number greatly improves and the computation efficiency rises in the simulation of multidi⁃mensional problems.Therefore,the proposed scheme makes an accurate,efficient and robust numerical method.