Numerical simulation of cavity flows based on transformed equations
A new numerical algorithm is applied to simulate two-dimensional lid-driven cavity flows. In this new algorithm, the momentum equations are first transformed using an exponential function to eliminate the convection terms in the equations. Then a central differencing scheme is employed to discretize the transformed equations. The cavity flows studied in this work include those with non-zero velocity component in the y-direction on the upper and lower boundaries. The results for the velocity components along the geometric centerline, stream function patterns, and vorticity contours are presented and discussed. The predicted results are in excellent agreement with benchmark solutions.