不可压黏性流问题的无网格法分析

不可压缩黏性流问题一般采用Navier-Stokes方程来描述，基于加权残值法，推导了问题的无网格伽辽金法（EFGM）离散Navier-Stokes方程，在时间域上采用分步方法计算，速度和压力由相互独立的方程以解耦的形式求解，并采用同阶移动最小二乘近似，在每一时间步中，对压力解和速度解采用了Newton-Raphson迭代法进行修正，最后将所得到的方法应用到剪切驱动空腔流问题中，验证了方法的有效性，且解的精度高、稳定性好。

AN ANALYSIS OF INCOMPRESSIBLE VISCOUS FLOWS BY MESHLESS METHOD

The element-free Galerkin method is applied to solve the incompressible viscous flows problem, which is described by the Navier-Stokes equation. The discrete formulation of the element-free Galerkin method is obtained by a weighted residual method, and the fractional step method in time domain is adopted. This method is useful because one may use the same moving least-squares(MLS) interpolation functions for both velocity and pressure, and velocity and pressure are solved by independent equations, respectively. The Newton-Raphson iterative method is used for the velocity and pressure in each time step. Finally, the method is applied to the shear-driver cavity flow to verify the validity and accuracy of this study.