不可压缩流基于块预处理的并行有限元计算

Parallel Finite Element Computation of Incompressible Viscous Flows Based on Block Preconditioning Strategy

  • 摘要: 发展了一个模拟非定常不可压缩粘性流的并行有限元求解器,时间离散使用具有二阶精度的隐式中点格式,基于三维非结构四面体网格剖分,使用高阶混合有限元离散速度场(P2)和压力场(P1).全离散格式产生的代数方程组是大型、稀疏、非对称和病态的,基于修正的压力对流扩散预处理(PCD)和精心设计的子问题迭代执行策略,采用预处理的GMRES迭代法来高效求解线性方程组.利用相同的子问题迭代策略,同时给出基于最小二乘交换子(LSC)预处理的并行效率对比.大量数值算例验证了算法的精度、可扩展性和可靠性.三维驱动方腔流模拟结果(Re=3200.0)清晰地显示了方腔流中主涡(PE)、下游二次涡(DSE)、上游二次涡(USE)、侧壁涡(EWV)和TGL涡的存在.

     

    Abstract: A parallel finite element solver is developed for simulation of the unsteady incompressible viscous flows. Implicit mid-point scheme is used to discretize time variable. Based on unstructured grid, velocity and pressure are discretized by classical P2-P1 Taylor-Hood mixed finite element. Resulting linear algebraic systems are large-scale, sparse, non-symmetric and ill-conditioned. Using a specially designed iterative strategy, it is solved by preconditioned GMRES method with modified pressure-convection-diffusion(PCD) preconditioner. A number of numerical experiments verify scability and validity of the solver. Especially, driven cavity flow simulation in 3D (Re=3200.0) clearly shows existence of primary eddy, downstream secondary eddy, upstream secondary eddy, end-wall vortices and T-G-like vortices. A parallel efficiency comparison with least-squares commutator(LSC) preconditioner is also given.

     

/

返回文章
返回