不可压热流体的离散统一气体动理学简化算法

A simplified discrete unified gas kinetic scheme for incompressible thermal flows

离散统一气体动理学算法是一种适用于连续流和稀薄流的统一数值算法,具有良好的数值稳定性和较高的数值精度,但算法结构较为复杂,计算效率有待提升。针对不可压缩热流体流动,在原始的离散统一气体动理学算法的基础上,使用梯形法则代替中点法则求解对流项,提出一个简化的离散气体动理学算法,用二维自然对流进行数值模拟。理论分析和计算结果表明,对于二维热对流问题的求解,和原始算法相比,改进算法在保障稳定性和数值精度下,计算效率提升了30%左右。

The discrete unified gas kinetic scheme(DUGKS)is a finite volume numerical algorithm suitable for continuum and rarefied flows,which has excellent numerical stability and high precision.However,the algorithm structure of DUGKS is complicated,there is still space for improvement.In this paper,a simplified DUGKS is proposed for incompressible thermal flows,which uses the trapezoidal rule instead of the midpoint method to solve the convection term.To verify our algorithm,the two-dimensional natural convection flow is simulated with the simplified DUGKS.Theoretical analysis and simulation results show that for the solution of the two-dimensional heat convection problem,the new method has the comparable numerical stability and computational accuracy as the origin DUGKS,but the computational efficiency can be improved about 30%.