Open AccessThe meshless local Petrov-Galerkin method for simulating unsteady incompressible fluid flow
Author(s) -
C. Sataprahm,
Anirut Luadsong
Publication year - 2014
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2013.10.002
Subject(s) - petrov–galerkin method , mathematics , poisson's equation , gaussian , compressibility , regularized meshless method , weight function , mathematical analysis , flow (mathematics) , galerkin method , function (biology) , incompressible flow , finite element method , geometry , mechanics , physics , singular boundary method , quantum mechanics , evolutionary biology , biology , boundary element method , thermodynamics
AbstractThis article presents a numerical algorithm using the Meshless Local Petrov-Galerkin (MLPG) method for the incompressible Navier–Stokes equations. To deal with time derivatives, the forward time differences are employed yielding the Poisson’s equation. The MLPG method with the moving least-square (MLS) approximation for trial function is chosen to solve the Poisson’s equation. In numerical examples, the local symmetric weak form (LSWF) and the local unsymmetric weak form (LUSWF) with a classical Gaussian weight and an improved Gaussian weight on both regular and irregular nodes are demonstrated. It is found that LSWF1 with a classical Gaussian weight order 2 gives the most accurate result