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

Authors:
Kazufumi Ito;Zhonghua Qiao
Affiliations:
Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, USA;Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695, USA
Venue:
Journal of Computational Physics
Year:
2008

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Abstract

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.