三维顶板驱动方腔流的有限元数值模拟

Numerical simulation of 3D lid-driven cubic cavity flow by two kinds of schemes with finite element method

该文基于PETScFEM开源代码,采用两种有限元方法计算不同雷诺数(1000、3200和10000)下的三维顶板驱动方腔流问题,并对计算结果进行比较。一种方法是整体求解NS方程,对流项采用streamline upwind Petrov-Galerkin格式(SUPG)进行稳定,不可压条件采用pressure stabilized Petrov-Galerkin格式(PSPG)进行稳定;另一种方法是分步有限元算法,基于poisson投影对速度和压力进行解耦。两种方法中均采用速度和压力同阶插值。计算结果表明,两种方法均能得到较好的结果,但分步算法对时间步长有一定限制。

Two kinds of numerical schemes with finite element method are applied to the simulation of 3D lid-driven cubic cavity flow at different Reynolds numbers （1000, 3200 and 10000）. The calculation is based on the open source codes PETScFEM. One scheme is solving the Navier-Stokes equations monolithicly, while the convection term is stabilized by streamline upwind Petrov-Gaterkin （SUPG） operator, and the incompressible condition is stabilized by pressure stabilized Petrov-Gaterkin （PSPG） operator. The other one is the fractional step method, which decouples the velocity and pressure field by introducing the Poisson projection. Linear equal-order-interpolation velocity-pressure elements are applied to both schemes. The numerical results show that both schemes are suitable for the simulation of the 3D lid-driven cubic cavity flow. However, there is a lower bound for the time step of the fractional step method for stability reasons.