混合网格DG方法及其在高超声速流动模拟中的应用

THE APPLICATION OF DISCONTINUOUS GALERKIN METHOD ON HYBRID GRIDS FOR HYPERSONIC FLOWS

混合网格高精度DG方法在高超声速模拟中面临诸多困难,其中以稳定性问题尤为突出.本文在二维三角形、四边形网格上构建了直到4阶的高精度DG方法,用于模拟可压缩无粘流动.采用Cockburn等人提出的斜率限制器和基于密度的Krivodonova间断探测器技术解决高超声速流动计算中的激波捕捉问题.首先通过等熵涡算例和Lax激波管问题对方法进行了精度与激波捕捉效果的验证,然后将其应用到双压缩拐角9马赫高超声速流动模拟中.模拟结果显示,高阶DG方法准确捕捉了激波相互作用结构,与文献2阶有限体积方法相比,在很少的网格上获得了令人满意的壁面压力数据.本文研究还表明,基于密度的Krivodonova间断探测器在含膨胀波的高超声速流动计算中的应用可能有一定局限性.

Significant challenges exist in the application of high order disconinuous Calerkin method on mixed unstructured grids for hypersonic flows, especially the stability issue. The discon- tinuous Galerkin method until 4th order accurate was formulated on 2D triangular and quadrilateral elements to simulate compressible inviscid flows. The slop limiter,proposed by Cockburn and Shu, along with the density based Krivodonova shock detector were used to smoothly capture the strong shocks of hypersonic flows. The isentropic vertex problem and Lax＇s problem were introduced to verify the order of accuracy and shock computation ability. Then the method was applied to the 9 mach hypersonic flow across a double wedge. The results show that the shock interaction structure is clearly captured and satisfactory pressure distritution on the wall is obtained using much coarser mesh than the one the 2nd order finite volume method used. The double wedge simulation also implies that the density based Krivodonova detector may have some limitations for hypersonic flows with expansion waves presented.