A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach

This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.