高精度有限体积格式在三维曲线坐标系下的应用

为了构造在光滑区具有较高分辨率并且可以无振荡捕捉激波的高精度有限体积格式,同时降低格式在模板选择上遇到的困难,基于逐维重构方法,发展了结构网格下的高精度有限体积格式,并将这一格式推广到三维曲线坐标系下,从而可以适应相对复杂外形下的计算。为充分验证格式的有效性,选取一系列典型算例进行计算:在等熵涡输运和二维喷管流动中验证了格式的精度可以达到设计精度;在双马赫反射问题中格式也表现出良好的捕捉激波的能力。数值计算表明,上述格式在曲线网格上具有较高的数值精度和鲁棒的激波捕捉能力,适用于流体力学方程的计算。

High-order finite volume schemes in three-dimensional curvilinear coordinate system

In order to develop a high-order finite volume method, a high-order finite volume scheme is developed, based on the dimension-by-dimension reconstruction method. This scheme has the abilities of keeping high fidelity in smooth region and well capturing discontinuities. The dimension-by-dimension reconstruction method can also overcome the difficulty in choosing stencils. In this paper, this scheme is also extended to the curvilinear coordinate system, which is suitable for the relatively complex configurations. In order to validate the numerical scheme, some test cases are used. In the cases of the isentropic vortex and two-dimensional channel flow, it is found that the designed order of accuracy can be achieved. In the double Mach problem, it is proved that the scheme can well capture the discontinuities. The test cases show the efficiency in the simulations of the computational fluids dynamics (CFD).