modeling incompressible lid-driven cavity using implicit finite difference method

The current study of incompressible flow characteristics in a confined square cavity, known as the lid-driven cavity model, is an essential step in constructing several related applications. this study uses the fully implicit finite difference method in a 2d algorithm to assess the lid-driven cavity model. the governing equation is solved in stream function-vorticity terms using the finite difference method for the spatial derivatives and the forward euler method for the time derivatives. the developed numerical model effectively solves low to moderate reynolds numbers, including 102, 4×102, 103, and 3.2×103, with a uniform grid structure. then, a non-uniform grid is also developed to solve high reynolds numbers with re = 5×103, 7.5×103, and 104. the model of flow characteristics at various re numbers is effectively solved, with varying results in velocity distribution, streamline patterns, and vorticity contours. this study exhibits appropriate validation consistency with earlier research utilizing different numerical methods.