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Solution of Stokes equations by moving least squares

✍ Scribed by Desimone, Hernan ;Urquiza, Santiago ;Arrieta, Hernan ;Pardo, Enrique

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 194 KB
Volume: 14
Category: Article
ISSN: 1069-8299
DOI: 10.1002/(sici)1099-0887(1998100)14:10<907::aid-cnm197>3.0.co;2-o

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✦ Synopsis

In this paper a numerical solution for incompressible Stokes equations using moving least-squares interpolators is developed. This approach does not require an element discretization; just a cloud of points is necessary. This is very attractive for 3D problems and deformable domains. First, taking into consideration that Dirichlet boundary conditions are not applicable a posteriori as in ®nite elements, a variational weak formulation that includes all kinematic restrictions (Dirichlet and incompressibility) is derived. Then the discretized resultant equations using a moving least-squares (MLS) interpolant for velocity and pressure ®elds are presented. Finally, the performance of the MLS interpolation is analysed by comparing numerical and analytical solutions, paying attention to the selection of the polynomial degree for the basis function and its orthogonalization. Dierent aspects of numerical implementation are discussed.

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