【摘要】 Navier-Stokes方程是一类非线性的鞍点问题,在高Reynolds数流的情形下,标准Galerkin有限元方法会导致数值伪震荡.迎风有限元方法在算法结构上表征了流体"上游"决定"下游"的流动性态,它能够有效地消除高Reynolds数流的对流占优扩散所产生的非物理震荡.基于此,将Navier-Stokes方程的对流项采用有限体积框架下的迎风离散,对其它项仍使用Galerkin有限元离散,研究了二维定常Navier-Stokes方程的数值求解,编程藉助于有限元程序自动生成软件FEPG.通过对方腔流动和圆柱绕流问题与基准测试已有数值结果的比较,验证了所构造方法的可行性和有效性.更多还原

【Abstract】 Navier-Stokes equations set is a nonlinear and saddle-point problem.In case of a higher Reynolds number,Galerkin FEM simulation of N-S equations may result in inaccurate oscillations. Upwind finite element method,which have the fluid property of downstream determined by upstream in the algorithm structure,can efficiently eliminate the oscillations brought by dominate influence of the convective term in the high Reynolds number flow. Therefore,stationary Navier-Stokes Equations can be directly numerically simulated by the finite element-finite volume upwind(only the convective term) methods.Results are acceptable compared with tests by others on the DFG 1995 Benchmark Problems of lid driven cavity and flow around a cylinder.更多还原