TY - JOUR

T1 - A novel mlpg-finite-Volume mixed method for analyzing stokesian flows & study of a new vortex mixing flow

AU - Avila, Ruben

AU - Han, Zhidong

AU - Atluri, Satya N.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Chaotic advection

KW - Meshless Local Petrov-Galerkin approach (MLPG)

KW - Stokesian flows

UR - http://www.scopus.com/inward/record.url?scp=79955694856&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79955694856

VL - 71

SP - 363

EP - 395

JO - CMES - Computer Modeling in Engineering and Sciences

JF - CMES - Computer Modeling in Engineering and Sciences

SN - 1526-1492

IS - 4

ER -