基于稀疏网格法的随机方腔流数值模拟研究

Numerical Simulations of Stochastic Cavity Flow Based on Sparse Grid

流动问题中存在大量随机因素,其影响会在流场内传播。多项式混沌方法是研究不确定性传播的高效方法之一。然而,随着不确定性变量的增多,全正交的多项式混沌方法计算量也会迅速增加。稀疏网格方法与多项式混沌方法的结合,成为主要研究发展方向。本文给出了稀疏网格生成方法,并用Gauss-Hermite积分规则构造多项式混沌。基于OpenFOAM求解器进行二次开发,模拟了不同数量的不确定性量对随机方腔流动的影响,验证稀疏网格方法的精度及效率,并与全正交多项式混沌方法和蒙特卡洛计算结果进行了对比。结果表明,高维情况下稀疏网格法的效率和精度较全正交多项式混沌方法有所提高,为研究不确定性CFD方法提供新思路。

There are a lot of random factors in the flow problem,and the influence will propagate in the flow field.Polynomial chaos is one of the most efficient methods to study the propagation of uncertainties.However,as the number of non-deterministic variables increases,the computation cost of full orthogonal polynomial chaos increases rapidly.The combination of sparse grid method and non-intrusive polynomial chaos method has become the main research direction.In this paper,a sparse grid generation method is presented,and polynomial chaos are constructed by Gauss-Hermite integral rule.The second development has proceeded base on OpenFOAM,the influence of different amounts of uncertainties on stochastic cavity flow is simulated,the precision and efficiency of sparse grid method are verified,which are compared with full orthogonal polynomial chaos method and Monte Carlo.The results show that the efficiency and accuracy of sparse grid method are better than that of full orthogonal polynomial chaos method in high dimensions,which provide a new way to study the non-deterministic CFD method.