三维不可压流动有限元数值模拟

A FINITE ELEMENT METHOD FOR SIMULATING THREE-DIMENSION INCOMPRESSIBLE FLOW

用原始变量带涡量的伽辽金有限元法计算三维定常不可压Ｎ－Ｓ问题，克服了过去由于速度和压力导数不同阶而不得不采用不同阶插值函数的困难。引入牛顿法线化Ｎ－Ｓ方程，使得用有限元离散后的大型代数方程组线性化，用高斯－赛德尔迭代法求解。算例为三维方穴驱动和带潜入锥的固体火箭发动机燃烧室轴对称加质流动。三维方穴驱动的计算结果与文献值相近。

In this paper the Galerkin finite element method based on the velocit y-pressure-vort icity formulation is applied to 3D steady incompresible N-S problems.This method can surmount the difficulty having to adopt' unequal-order interpolations,due to the derivative of velocity and pressure unequal-order in the past.The Newton's method is employed to linearize N-S equations,the finite element method is used to obtain discretized equations.The system of algebraic equations is linear and is solved using the Gauss-Seidel iterative method.The flow in a half of 3D cubic cavity and the axisymmetrical flow adding mass in SRM chamber with submerged cone are calculated.The results of 3D cubic cavity are compared to the results of reference.