模拟可压缩流的高分辨率有限元法

采用经典的Galerkin方法对N-S方程进行空间离散,再以该半离散格式作为基本格式,参照Kuzmin的思想加入耗散与反耗散项,使所构造的格式具有局部极值不增(LED,Local Extremum Diminishing)性质.对上述半离散格式进行时间离散后所导出的稀疏线性代数方程组,采用了GMRES(Generalized Minimal Residual)迭代法进行求解.为验证所建立的格式及相应的程序,给出了激波管问题和绕圆柱与双椭球超声速流动问题的数值模拟结果. 

High resolution finite element procedure for compressible flows simulation

Spatial discretization of N-S equations was first deduced based on the classical Galerkin method.Taking the above semi-discretized formulation as the basic scheme,a diffusion and an associated anti-diffusion terms were then added,keeping the scheme to possess a local extremum diminishing(LED) property.After taking the time discretization of the above derived semi-discretized scheme,the resulting system of sparse linear algebraic equations was solved by utilizing generalized minimal residual(GMRES).In order to validate the developed scheme with associated code,numerical computations for the shock tube problems,as well as supersonic flows over a cylinder and a double ellipsoid were performed,which revealed that the developed scheme did provide high resolution results.