an alternating direction implicit method for modeling of fluid flow

This research includes of the numerical modeling of fluids in two-dimensional cavity. the cavity flow is an important theoretical problem. in this research, modeling was carried out based on an alternating direction implicit via vorticity-stream function formulation. it evaluates different reynolds numbers and grid sizes. therefore, for the flow field analysis and prove of the ability of the scheme, the numerical solution was carried out for different values of the reynolds numbers. also, the behavior of the vortex flow in cavity was predicted. this research compares results of applied numerical model with the results of chia et al. [1] and chen & pletcher [2]. comparing the results with those of the benchmarks show that alternating direction implicit is an effective and suitable formulation for the solution of the navier–stokes equations.