Abstract
We consider the steady state Stokes equations, describing low speed flow and derive estimates of the solution for various types of boundary conditions. We formulate the boundary conditions in a new way, such that the boundary value problem becomes non-singular. By using a difference approximation on a staggered grid we are able to derive a non-singular approximation in a direct way. Furthermore, we derive the same type of estimates as for the continuous case. Numerical experiments confirm the theoretical results.
Similar content being viewed by others
REFERENCES
Abdallah, S. (1987). Numerical solution for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid, I. J. Comput. Phys. 70, 182–192.
Barrett, R., Berry, M., Chan, T. F., Demmel, J., Donato, J., Dongarra, J., Eijkhout, V., Pozo, R., Romine, C., and Van der Vorst, H. (1994). Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, PA.
Gustafsson, B., and Nilsson, J. (2000). Fourth order methods for the Stokes and Navier-Stokes equations on staggered grids. Submitted to Frontiers of Computational Fluid Dynamics.
Harlow, F. H., and Welch, J. E. (1965). Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2181–2189.
Morinishi, Y., Lund, T. S., Vasilyev, O.V., and Moin, P. (1998). Fully conservative higher order finite difference schemes for incompressible flow. J. Comp. Phys. 143, 90–124.
Strikwerda, J. C. (1984). Finite difference methods for the Stokes and Navier-Stokes equations. SIAM J. Sci. Stat. Comput. 5, 56–68.
Tau, E. Y. (1992). Numerical solution of the steady Stokes equations. J. Comput. Phys. 90, 190–195.
Wesseling, P., Segal, A., and Kassels, C. G. M. (1999). Computing flows on general three-dimensional nonsmooth staggered grids. J. Comp. Phys. 149, 333–362.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gustafsson, B., Nilsson, J. Boundary Conditions and Estimates for the Steady Stokes Equations on Staggered Grids. Journal of Scientific Computing 15, 29–59 (2000). https://doi.org/10.1023/A:1007545718304
Issue Date:
DOI: https://doi.org/10.1023/A:1007545718304