Solution of the driven cavity problem in primitive variables using the SMAC method

摘要

The equations of two-dimensional incompressible fluid flow in a square driven cavity were solved in terms of primitive variables and stream functions. A Simplified Marker-and-Cell method was used with forward time and centered space (FTCS) differencing and with modified forward time and centered space (MFTCS) differencing. The problem could not be solved for a Reynolds number of 100 with FTCS differencing because of stability limitations. For a Reynolds number of 10, the results are found to be inaccurate because of the inability of the pressure solver to converge to small tolerances. The MFTCS differencing seemed to relax the stability restriction on time step, but the limit on cell Reynolds number was retained. A lower order boundary condition on pressure resulted in marginal improvement. Tables (data) of flow velocities are included.