计算三维边界层分离流动的一种双向推进有限元格式

 本文提出一种适用于兰维边界层正、逆向问题的有限元格式。格式采用了对壁面法向进行Galerkin加权,沿壁面进行子域加权并作双向推进的弱解形式。它不仅可节约内存,同时还可通过与等参元素的结合应用给出CFL条件的显式表述,保证了问题的快速求解。进行逆模态计算时,以位移厚度作约束条件,通过Lagrange乘子直接引入边界层方程的有限元类比中进行整体求解。算例表明该格式模拟三维边界层流动是经济有效的。

A BI-DIRECTIONAL MARCHING FINITE ELEMENT ALGORITHM FOR THREE-DIMENSIONAL BOUNDARY LAYER SEPARATION FLOW COMPUTATIONS

A finite element algorithm is proposed for solving the direct- and inverse-problems of three-dimensional boundary layers. The algorithm is constructed based on a Galerkin discretization along the traversal direction across the boundary layer, and a subdomain discretization in conjunction with a bi-directonal marching procedure along the body surface. The present algorithm would yield an explicit form of the CFL condition by incorporating the isoparametric elements, and thus provide an assurance for fast-solving the problems of both modes. For the inverse mode, the displacement thicknesses are considered as a set of constrains, and are integrated into the finite element analog of the boundary layer equations via Lagrange multipliers. Several test cases are computed by the present technique, and the results show that the present technique do provide an economical as well as efficient tool for computing three-dimensional boundary layer flows.