An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow. (English) Zbl 1428.76146
Summary: In this paper, we develop a meshless collocation scheme for the numerical solution of magnetohydrodynamics (MHD) flow equations. We consider the transient laminar flow of an incompressible, viscous and electrically conducting fluid in a rectangular duct. The flow is driven by the current produced by electrodes placed on the walls of the duct. The method combines a meshless collocation scheme with the newly developed Discretization Corrected Particle Strength Exchange (DC PSE) interpolation method. To highlight the applicability of the method, we discretize the spatial domain by using uniformly (Cartesian) and irregularly distributed nodes. The proposed solution method can handle high Hartmann (Ha) numbers and captures the boundary layers formed in such cases, without the presence of unwanted oscillations, by employing a local mesh refinement procedure close to the boundaries. The use of local refinement reduces the computational cost. We apply an explicit time integration scheme and we compute the critical time step that ensures stability through the Gershgorin theorem. Finally, we present numerical results obtained using different orientation of the applied magnetic field.
MSC:
| 76M22 | Spectral methods applied to problems in fluid mechanics |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
Keywords:
meshless point collocation; discretization corrected particle strength exchange (DC PSE); unsteady MHD; Hartmann number; explicitSoftware:
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