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A novel MLPG-Finite-Volume Mixed Method for Analyzing Stokesian Flows & Study of a new Vortex Mixing Flow

Ruben Avila1, Zhidong Han2, Satya N. Atluri3
Departamento de Termofluidos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, Mexico D.F., C.P. 04510, ravila@servidor.unam.mx, Center for Aerospace Research & Education, University of California, Irvine.
Center for Aerospace Research & Education, University of California, Irvine.
Center for Aerospace Research & Education, University of California, Irvine, satluri@uci.edu.

Computer Modeling in Engineering & Sciences 2011, 71(4), 363-396. https://doi.org/10.3970/cmes.2011.071.363

Abstract

The two dimensional steady state Stokes equations are solved by using a novel MLPG-Mixed Finite Volume method, that is based on the independent meshless interpolations of the deviatoric velocity strain tensor, the volumetric velocity strain tensor, the velocity vector and the pressure. The pressure field directly obtained from this method does not suffer from the malady of checker-board patterns. Numerical simulations of the flow field, and trajectories of passive fluid elements in a new complex Stokes flow are also presented. The new flow geometry consists of three coaxial cylinders two of smaller diameter, that steadily rotate independently, inside a third one of elliptical cross section, whose wall slides at a constant angular speed. We show, by performing detailed comparisons with analytical solutions, that the present mixed-MLPG method, coupled with an algorithm to track passive massless fluid elements, provides accurate results for the pressure and velocity fields, and for their spatial derivatives along the streamlines of the flow domain.

Keywords

Meshless Local Petrov-Galerkin approach (MLPG), Chaotic advection, Stokesian flows.

Cite This Article

Avila, R., Han, Z., Atluri, S. N. (2011). A novel MLPG-Finite-Volume Mixed Method for Analyzing Stokesian Flows & Study of a new Vortex Mixing Flow. CMES-Computer Modeling in Engineering & Sciences, 71(4), 363–396.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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