The application of the boundary element method to the magnetohydrodynamic duct flow
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
The application of interpolating MLS approximations to the analysis of MHD flows
Finite Elements in Analysis and Design
Maximum principle and convergence analysis for the meshfree point collocation method
SIAM Journal on Numerical Analysis
Fundamental solution for coupled magnetohydrodynamic flow equations
Journal of Computational and Applied Mathematics
An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems
Journal of Computational Physics
An Introduction to Meshfree Methods and Their Programming
An Introduction to Meshfree Methods and Their Programming
A DRBEM solution for MHD pipe flow in a conducting medium
Journal of Computational and Applied Mathematics
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In this article a numerical solution of the time dependent, coupled system equations of magnetohydrodynamics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approximation of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collocation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform magnetic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for several Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form meshless methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov---Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L 驴, the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems.