Iterative Scheme for Navier-Stokes Equations Based on Operator Splitting

C. I. Christov

Email: christov@louisiana.edu
Postal address: Dept. of Mathematics, P.O. Box 1010, Lafayette, LA 70504-1010

The incompressible Navier-Stokes equations are considered and a new form of the Poisson equation for the pressure is proposed in which the continuity equation are explicitly acknowledged. A restriction of the continuity at the boundary is also used as boundary condition allowing one not pose artificial boundary conditions for the implicit pressure function. As a result, the matrix operator becomes better suited to the purposes of splitting when dealing with a coupled system for for the vector (u,v,w,p). A vectorial generalization of the splitting method is used which leaves the system coupled at each fractional time step. This approach gives us a strongly implicit scheme that is stable for wide range of time steps and iteration parameters. As featuring examples are considered the 3D steady and the 2D unsteady flow in a rectangular lid-driven cavity. The strong stability of the scheme allows obtaining reliable results for very high Reynolds numbers.