可压缩SIMPLE算法中密度的处理方法

Method of Dealing with Density in SIMPLE Algorithm for Compressible Flows

在可压缩流的计算中,针对准确有效地得到激波间断解一直是研究中的难点。由于密度对激波的分辨率具有重要影响,当用有限体积法在同位网格上采用离散Navier-Stokes方程时,为了保证稳定性,对流质量通量的计算中密度运用一阶迎风(FUD)格式进行插值,结果难以得到高分辨率的激波间断解。为了提高激波分辨率,改善计算精度,提出了对流性项中界面密度的计算方法,采用流质量通量与压力修正值方程源项里质量通量计算中界面密度的插值方法统一起来,都采用具有高分辨率格式。通过跨音速和超音速圆弧凸包两个算例的仿真,结果表明,方法有效地克服了FUD格式过扩散性的缺陷,又保持了FUD格式良好的稳定性,显著提高了激波分辨率,因而是一种能够改善计算精度的有效方法。

In the calculation of compressible flows, how to capture a high resolution shock has always been a challenge for researchers ever since. Density gives an extremely important influence over the resolution of shock, especial- ly in SIMPLE algorithm for compressible flows. When discretizing Navier-Stokes equations on collocated grids utili- zing finite-volume method, in consideration of stability, first order upwind （FUD） scheme is frequently adopted to compute cell-face density in the calculation of advection mass flux, which, however, results in severe smearing of shock wave if a shock is contained in the flow, showing the difficulty of obtaining a high resolution shock. In order to obtain a higher shock resolution and improve calculation accuracy, detailed discussion is placed on the computing method for cell-face density of convective terms in the present paper. Upwind biased high-resolution schemes are u- niformly applied to calculate cell-face density of both convective mass flux and mass flux in the source term of pres- sure correction equation. The numerical results of the two test cases about circular arc bump indicate that the presen- ted method substantially reduces the diffusivity of FUD scheme with no loss in stability and noticeably improves the resolution of shock waves. Therefore, conclusion can be made that it is an effective method to improve calculation ac- curacy.