A Numerical Simulation of Unsteady Lid Driven Cavity Flow With Moving Boundaries Using CMSIP

A two-dimensional, mathematical model is adopted to investigate the development of circulation patterns for compressible lid driven flows inside a rectangular cavity where the bottom of the cavity is free to move at a specified speed. A time and space dependent transformation is applied to the governing equations to obtain a rigid (non-moving) solution domain. The transformed equations are discretized for a uniform and orthogonal computational mesh using second order in space and first order in time finite difference schemes. The resulting nonlinear equations are then linearized using Newton’s linearization method. Finally, the set of algebraic equations that result from this process are put into a matrix form and solved using the Coupled Modified Strongly Implicit Procedure (CMSIP). Numerical experiments are carried out for various Reynolds numbers to verify the accuracy of the solution algorithm. Then the numerical simulations of lid driven flow inside the cavity is carried out for the unsteady case where the aspect ratio of the cavity is changed from 1 to 1.5 at a constant speed. It is concluded that the proposed model is successful in predicting the unsteady characteristics of the primary vortex and the secondary vortices inside a cavity with moving bottom.