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Solving Stokes Equation in Plane Irregular Regions using an Optimal Consistent Finite Difference Scheme

Tinoco-Ruiz, J. G., F. Dominguez-Mota, S. Mendoza-Armenta and G. Tinoco-Guerrero

Research Notes, 20th International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 23-26 2011

IMR
PROCEEDINGS

20th International Meshing Roundtable
Paris, France
October 23-26, 2011

Facultad de Ciencias Fisico Matematicas Universidad Michoacana de San Nicolas de Hidalgo Edificio \B", Ciudad Universitaria, Morelia, Mexico 58040
Email: dmota@umich.mx

Summary
Historically, finite difference Schemes (FDS) defined in logically rectangular grids have been widely used to get numerical approximations to the solution of partial differential equations in simple domains, i.e., rectangular regions or those suitable to be decomposed in rectangles, but when the region is not of this kind, the classical schemes can not longer be applied. However, the development of efficient methods for meshing irregular planar regions using quadrilateral elements allows new schemes to be defined. In this paper, in order to solve numerically Stokes equation on an irregular domain using finite differences, we show the application of a simple scheme derived from a local optimization problem.

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