Parallel Meshless EFG Solution for Fluid Flow Problems

Abstract

ABSTRACT This article deals with the parallel computing solution of fluid flow problems using a meshless element-free Galerkin (EFG) method. The EFG method utilizes moving least-square (MLS) approximants to approximate the unknown field variables. The MLS approximant consists of three components: a weight function, a basis function, and a set of nonconstant coefficients. A new parallel algorithm is proposed for the EFG method. The code has been written in FORTRAN language using MPI message passing library and implemented on a MIMD (multiple-instruction multiple-data)-type PARAM 10000 supercomputer. The code has been validated by solving three model fluid flow problems. A comparison is made among the results (velocities values) obtained by the EFG method with those obtained by the finite-element method (FEM) at a few typical locations. For 8 processors, speedup and efficiency have been obtained as 2.73 and 34.22% for N = 1,552 in 1-D (Example I), 7.20 and 90.00% for N = 1,462 in 2-D (Example II), and 7.30 and 91.27% for N = 1,346 in 2-D (Example III), respectively.