Partitioned second order method for magnetohydrodynamics in Elsässer variables. (English) Zbl 1394.76149
Summary: Magnetohydrodynamics (MHD) studies the dynamics of electrically conducting fluids, involving Navier-Stokes equations coupled with Maxwell equations via Lorentz force and Ohm’s law. Monolithic methods, which solve fully coupled MHD systems, are computationally expensive. Partitioned methods, on the other hand, decouple the full system and solve subproblems in parallel, and thus reduce the computational cost.
This paper is devoted to the design and analysis of a partitioned method for the MHD system in the Elsässer variables. The stability analysis shows that for the magnetic Prandtl number of order unity, the method is unconditionally stable. We prove the error estimates and present computational tests that support the theory.
This paper is devoted to the design and analysis of a partitioned method for the MHD system in the Elsässer variables. The stability analysis shows that for the magnetic Prandtl number of order unity, the method is unconditionally stable. We prove the error estimates and present computational tests that support the theory.
MSC:
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 35Q30 | Navier-Stokes equations |
| 35Q61 | Maxwell equations |
Keywords:
magnetohydrodynamics; Elsässer variables; partitioned scheme; backward differentiation formula BDF2; stability; long time stability; error estimatesReferences:
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