An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems

Journal Article · Fri Nov 20 04:00:00 EST 2009 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2009.07.031· OSTI ID:21308121

Skouras, E D ^[1]

---

1. Department of Chemical Engineering, University of Patras, GR 26500, Rion (Greece)

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially conducting walls, having rectangular, circular, elliptical or even arbitrary cross sections. MPC is a truly meshless and computationally efficient method. The maximum principle for the discrete harmonic operator in the meshfree point collocation method has been proven very recently, and the convergence proof for the numerical solution of the Poisson problem with Dirichlet boundary conditions have been attained also. Additionally, in the present work convergence is attained for Neumann and Robin boundary conditions, accordingly. The shape functions are constructed using the Moving Least Squares (MLS) approximation. The refinement procedure with meshless methods is obtained with an easily handled and fully automated manner. We present results for Hartmann number up to 10{sup 5}. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the exact solution and the conventional FEM and BEM, for the Dirichlet, Neumann and Robin boundary conditions of interior problems with simple or complex boundaries.

• OSTI ID: 21308121
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 21 Vol. 228; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ALGORITHMS
APPROXIMATIONS
BOUNDARY CONDITIONS
CONVERGENCE
CROSS SECTIONS
DIRICHLET PROBLEM
EXACT SOLUTIONS
FUNCTIONS
GEOMETRY
HARTMANN NUMBER
LEAST SQUARE FIT
MAGNETOHYDRODYNAMICS