二维定常不可压缩粘性流动N-S方程的数值流形方法

Numerical manifold method for steady incompressible viscous 2D flow Navier-Stokes equations

将流形方法应用于定常不可压缩粘性流动N-S方程的直接数值求解,建立基于Galerkin加权余量法的N-S方程数值流形格式,有限覆盖系统采用混合覆盖形式,即速度分量取1阶和压力取0阶多项式覆盖函数,非线性流形方程组采用直接线性化交替迭代方法和Nowton-Raphson迭代方法进行求解。将混合覆盖的四节点矩形流形单元用于阶梯流和方腔驱动流动的数值算例,以较少单元获得的数值解与经典数值解十分吻合。数值实验证明,流形方法是求解定常不可压缩粘性流动N-S方程有效的高精度数值方法。

Manifold method for direct numerical solution of steady incompressible viscous Navier-Stokes equations is developed in this paper.Where numerical manifold schemes are derived based on Galerkin weighted residuals method,mixed cover with the first order polynomial functions for velocity components and constant function for pressure is adopted in finite cover system,and nonlinear manifold equations are solved by direct iteration and Nowton-Raphson iteration methods.As an application,mixed cover 4-node rectangular manifold element is used for computation and analysis of flow in square chamber and flow past a step,numerical solutions obtained with few elements are in very good agreement with classical data.Numerical testes indicate that manifold method is an effective and high order accurate numerical method for Navier-Stokes equations of steady incompressible viscous flow.