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A meshfree method for incompressible fluid dynamics problems
Author(s) -
Tsukanov I.,
Shapiro V.,
Zhang S.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.760
Subject(s) - meshfree methods , compressibility , mathematics , scalar (mathematics) , interpolation (computer graphics) , stream function , boundary (topology) , computation , mathematical optimization , mathematical analysis , computer science , geometry , finite element method , algorithm , physics , motion (physics) , mechanics , vorticity , artificial intelligence , vortex , thermodynamics
We show that meshfree variational methods may be used for the solution of incompressible fluid dynamics problems using the R ‐function method (RFM). The proposed approach constructs an approximate solution that satisfies all prescribed boundary conditions exactly using approximate distance fields for portions of the boundary, transfinite interpolation, and computations on a non‐conforming spatial grid. We give detailed implementation of the method for two common formulations of the incompressible fluid dynamics problem: first using scalar stream function formulation and then using vector formulation of the Navier–Stokes problem with artificial compressibility approach. Extensive numerical comparisons with commercial solvers and experimental data for the benchmark back‐facing step channel problem reveal strengths and weaknesses of the proposed meshfree method. Copyright © 2003 John Wiley & Sons, Ltd.