计算流体力学中非协调网格的隐式插值格式

Implicit interpolation scheme for non-conforming meshes in computational fluid dynamics

该文针对计算流体力学中出现的非协调网格耦合问题,提出了一种隐式插值格式。在不同子域间建立插值关系,针对变量的插值条件可视为Dirichlet传输条件,同时对代数方程组中的系数矩阵和右端项进行重新构建,以此来施加Neumann条件,从而实现计算域中不同网格的耦合。与现有的非协调网格插值方法相比,该方法直接重构代数方程组,摆脱了问题类型、网格形式、离散格式和求解器的限制,且不引入任何额外的自由度或迭代,简单高效,普适性强。并通过三个经典算例,验证了基于该插值格式的非协调网格数值模型具有较好的稳定性,计算结果与前人的实验结果和数值计算结果也吻合良好。

An implicit interpolation scheme is proposed to solve the problem of non-conforming meshes coupling in computational fluid dynamics.The interpolation relations between different subdomains are established,and the interpolation conditions for variables can be regarded as Dirichlet transmission conditions.At the same time,the coefficient matrix and the right hand side in the algebraic equations are reconstructed to impose Neumann conditions,so as to realize the coupling of different grids in the computational domain.Compared with the existing non-conforming meshes interpolation methods,this method reconstructs algebraic equations directly,gets rid of the limitations of problem type,grid form,discrete scheme and solver,and does not introduce any additional degrees of freedom or iteration,which is simple,efficient and has strong universality.Three classical numerical examples are used to verify the stability of the non-conforming meshes numerical model based on the proposed interpolation scheme,and the calculated results are in good agreement with the previous experimental and numerical results.