Abstract
This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.
Highlights
The flow of a conducting fluid in the presence of a magnetic field is termed as magnetohydrodynamics (MHD)
Since compressibility effects play a key role in applications such as magneto-gas dynamics, in this work, we focus on developing a MHD strategy for compressible fluids
We use higher order interpolation functions for the velocity and magnetic fields, as compared to the pressure, density, and temperature field variables. This ensures the satisfaction of the inf-sup stability conditions
Summary
The flow of a conducting fluid in the presence of a magnetic field is termed as magnetohydrodynamics (MHD). The formulation is based on primitive flow variables, such as velocity, density, temperature, pressure, and the magnetic field, which makes the implementation simple. In contrast to the work in references [1,2,4,5,6,7,8] that use a stabilized formulation, we use a stable formulation based on an appropriate choice of interpolations for the various field variables. We use higher order interpolation functions for the velocity and magnetic fields, as compared to the pressure, density, and temperature field variables. This ensures the satisfaction of the inf-sup stability conditions. We first present the equations for the magnetic fields, and the coupled equations to be solved on the entire domain
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