浸入式贴体网格边界方法

提出一种基于重叠网格的浸入式边界方法,用以模拟复杂的三维黏性跨声速流动。该方法采用一套固定的笛卡儿正交网格,用以主流的求解;采用一套可以移动的贴体等距面网格,用以拟合或者离散物面的作用力,通过空间插值,实现两套网格重叠部分的信息传递。分析了浸入式贴体网格边界方法的优势,介绍了贡献单元的寻找策略和物理通量的插值方法。流场求解采用Spalart-Allmaras带湍流模型的Navier-Stokes方程组,其中对流项采用流通矢量分裂和5阶WENO(weighted essentially non-oscillatory)-Z格式离散,黏性项采用6阶中心差分格式离散,时间项采用龙格库塔显式格式离散。数值验证算例表明:该方法具备高于4阶的空间求解精度，并适用于刚体动网格非定常流场模拟,且无需更新网格形状。等距面贴体网格生成过程简单,避免了繁琐的人工调节过程,与笛卡儿网格结合,可提供足够的壁面附近网格密度,同时有效减少了网格总量需求。

Immersed body-fitted meshes boundary method

An immersed boundary method combined with overset meshes on surface was proposed to simulate three-dimensional viscous compressible flow.Orthogonal Cartesian meshes were adopted to simulate the mainstream, and the body-fitted meshes immersed in the Cartesian meshes were adopted to simulate the viscous flow near the surface. The flow field information of the overlapped regions was transmitted to each other through spatial interpolation.The advantages of the immersed body-fitted meshes boundary method were summarized. Strategies for finding contribution units and interpolating flow information were introduced in detail.The Navier-Stokes equations with Spalart-Allmaras turbulence model were used to solve the flow field. The convection terms were discretized by flow vector splitting method and 5th order WENO (weighted essentially non-Oscillatory)-Z scheme, while the viscosity terms were discretized by 6th order central difference scheme. The time term was discretized by Runge Kutta explicit scheme.The numerical verification showed that spatial precision of this method was at least 4th order. This method is suitable for the unsteady flow simulation of moving rigid meshes without the need to update the mesh shape. The equidistant surface body-fitted meshes generation process is simple enough to avoid the tedious manual adjustment process. Combined with the Cartesian meshes, it can provide sufficient mesh density near the wall and effectively reduce the total mesh number demand.