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

作者：Zhang Zheng Rong^*; Zhang Xiang Wei

来源：Chinese Journal of Computational Mechanics, 2010, 27(3): 415-421.

• 2D flow
• Constant functions
• Direct iteration
• Finite cover
• First order
• Galerkin
• High order
• Incompressible viscous flows
• Incompressible viscous Navier-Stokes equation
• Iteration method
• Manifold elements
• Nonlinear manifolds
• Numerical manifold method
• Numerical solution
• Velocity components
• Weighted residuals method

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.

• 出版日期2010