基于指数插值的浸没边界法在可压缩流模拟中的应用研究

由于浸没边界法在处理复杂外形和动态问题时具有极强的灵活性和便利性，因而受到广泛的关注。在当前浸没边界法的研究和应用中，主要工作集中在关于中/低雷诺数和不可压流动的模拟。本文引入 Choi 等提出的指数插值法对目标点速度进行插值，并根据多项式插值和 Crocce-Busemann 关系式等确定目标点压力和温度，并借鉴直角网格法中的虚拟网格法计算物面内的流动变量，建立了适用于可压缩流动的浸没边界法。通过亚、跨声速段翼型绕流和超声速圆柱绕流算例对方法进行验证，结果显示在 k 值取值合适时模拟结果与实验数据较为吻合。通过对相关算例网格收敛性分析，证明了本文发展的浸没边界法具有较高的精度。文中各算例的模拟结果表明，此方法能准确捕捉亚、跨、超声速绕流问题中的各类流动结构，适用于可压缩流动的模拟。

The application of power-law interpolation based immersed boundary method in compressible flow simulation

The immersed boundary method(IBM)was rapid developed in recent years because of its flexibility for complex configurations and moving bodies.Up to date,most of the resear-ches on IB method focused on the incompressible flow due to the limitation of the interpolation method.The current research applied the Choi’s power-law interpolation and the Crocce-Buse-mann relationship for the velocity and temperature approximation in the objective cells.The ghost cell method was also used for computing the variables at the cells in the body.The subson-ic/transonic NACA0012 airfoil compressible cases and 2D supersonic cylinder benchmark cases were chosen for method validation.The numerical result of these benchmark cases with proper parameter k compared well with the experimental data.The mesh convergence of the new method has also been proved.The analysis and discussion show that the method is suitable for compressi-ble flow simulation.