Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Mixed finite element methods for stationary incompressible magneto–hydrodynamics
Numerische Mathematik
Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems
SIAM Journal on Numerical Analysis
Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods
Journal of Computational Physics
Approximation of the thermally coupled MHD problem using a stabilized finite element method
Journal of Computational Physics
Journal of Computational Physics
| Hi-index | 31.45 |
In this work, we present a stabilized formulation to solve the inductionless magnetohydrodynamic (MHD) problem using the finite element (FE) method. The MHD problem couples the Navier-Stokes equations and a Darcy-type system for the electric potential via Lorentz's force in the momentum equation of the Navier-Stokes equations and the currents generated by the moving fluid in Ohm's law. The key feature of the FE formulation resides in the design of the stabilization terms, which serve several purposes. First, the formulation is suitable for convection dominated flows. Second, there is no need to use interpolation spaces constrained to a compatibility condition in both sub-problems and therefore, equal-order interpolation spaces can be used for all the unknowns. Finally, this formulation leads to a coupled linear system; this monolithic approach is effective, since the coupling can be dealt by effective preconditioning and iterative solvers that allows to deal with high Hartmann numbers.