NUMERICAL SOLUTION OF THE NAVIER-STOKES EQUATION FOR INCOMPRESSIBLE FLOW IN RECTANGULAR CAVITY BY THE METHOD OF LINES

The numerical method of lines (MOL) is a numerical solu-tion technique for solveing the partial differential equations. In this paperthe two-dimensional unsteady Navier-Stokes equations for incompressiblelaminar flows are numerically investigated. The motion equations are pre-sented in the stream function-vorticity formulation. First, the Navier-Stokes equations in space are dicretized on a collocated gird by using themethod of lines (MOL) based on nite difference schemes. The time vari-able retained as a continuous variable and the discretized Navier-Stokesequations form a system of differential algebraic equations. This system isreduces to a system of ordinary differential equations (ODEs) after solvingthe discretized Poisson s equation. The resulting ODEs are solved by back-ward differentiation formulas (BDF). The flow in a rectangular lid drivencavity is considered as the model problem.

Keywords:

Navier-Stokes equation , Method of lines , Incompressible flow , Finite difference