Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

Journal Article · Wed Oct 01 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.05.038· OSTI ID:22382113

Morales, Jorge A. ^[1]; Leroy, Matthieu ^[2]; Bos, Wouter J.T. ^[1]; Schneider, Kai ^[2]

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1. LMFA-CNRS, École Centrale de Lyon, Université de Lyon (France)
2. M2P2-CNRS, Aix-Marseille Université, Marseille (France)

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analytical solutions. The test cases considered are two-dimensional Taylor–Couette flow, the z-pinch configuration, three dimensional Orszag–Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor–Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method.

• OSTI ID: 22382113
• Journal Information: Journal of Computational Physics, Vol. 274; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COMPARATIVE EVALUATIONS
COMPUTERIZED SIMULATION
COUETTE FLOW
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
FLEXIBILITY
INSTABILITY
MAGNETIC FIELDS
MAGNETOHYDRODYNAMICS
PERIODICITY
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS