最小二乘有限元法求解非定常应力的Navier-Stokes方程

为精确求解非定常层流问题,发展一种非定常速度-应力-压力的方法.采用牛顿法对非线性对流项进行线性化处理和预处理共轭梯度法,实现了非定常应力形式Navier-Stokes方程的求解.方腔层流流动比较发现,非定常应力形式比涡量形式与试验结果更加吻合,精度更高.该方法有效地解决亚格子应力项的问题,实现基于最小二乘有限元法的湍流求解.比较方腔湍流流动的试验与仿真结果,证明本文的方法具有可行性,为湍流大涡模拟计算打下基础.

Least-squares Finite Element Method for Unsteady Stress Formulation of Navier-Stokes Equations

To solve unsteady laminar flow problems,a method of velocity-stress-pressure formulation instead of velocity-vorticitypressure formulation is developed.With Newton's linearized method to linearize convective terms and preconditioned conjugate gradient method to solve equations,unsteady stress formulation of Navier-Stokes equations is solved.Comparison between numerical and experimental results of cavity laminar flow shows that result of stress formulation fits experiment better and has higher accuracy than vorticity formulation.The stress formulation can deal with subgrid stress with least squares finite element method.Comparison with experimental results of cavity turbulent flow reveals feasibility of the method.It lays a firm foundation for large eddy simulation computation.