Related papers: Computation of Magnetohydrodynamic Equilibria with…
We extend the Kreiss--Majda theory of stability of hyperbolic initial--boundary-value and shock problems to a class of systems, notably including the equations of magnetohydrodynamics (MHD), for which Majda's block structure condition does…
We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…
We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum,…
A numerical scheme is developed for systems of conservation laws on manifolds which arise in high speed aerodynamics and magneto-aerodynamics. The systems are presented in an arbitrary coordinate system on the manifold and involve source…
A new implementation for magnetohydrodynamics (MHD) simulations in full general relativity (involving dynamical spacetimes) is presented. In our implementation, Einstein's evolution equations are evolved by a BSSN formalism, MHD equations…
This work examines the controllability of planar incompressible ideal magnetohydrodynamics (MHD). Interior controls are obtained for problems posed in doubly-connected regions; simply-connected configurations are driven by boundary…
Models of magnetohydrodynamic (MHD) equilibia that for computational convenience assume the existence of a system of nested magnetic flux surfaces tend to exhibit singular current sheets. These sheets are located on resonant flux surfaces…
In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and…
Physical problems with a solution that can be expressed analytically are scarce; this holds even more true for problems set in a cosmological context. Such solutions are, however, invaluable tools for making comparisons between theory,…
The fully nonlinear (geometric and material) system of Field Dislocation Mechanics is reviewed to establish an exact analogy with the equations of ideal magnetohydrodynamics (ideal MHD) under suitable physically simplifying circumstances.…
We examine hyperbolicity of general relativistic magnetohydrodynamics with divergence cleaning, a flux-balance law form of the model not covered by our earlier analysis. The calculations rely again on a dual-frame approach, which allows us…
We consider the three-dimensional magnetohydrodynamics system forced by random noise. First, for smooth solutions in the ideal case, the cross helicity remains invariant while the magnetic helicity precisely equals the initial magnetic…
We present the theory, algorithms and implementation of a parallel finite-volume algorithm for the solution of the incompressible magnetohydrodynamic (MHD) equations using unstructured grids that are applicable for a wide variety of…
The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal…
Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We…
Magnetohydrostatic models of the solar atmosphere are often based on idealized analytic solutions because the underlying equations are too difficult to solve in full generality. Numerical approaches, too, are often limited in scope and have…
Axisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions. To this end a set of pertinent non-linear ODEs are…
Fully adaptive computations of the resistive magnetohydrodynamic (MHD) equations are presented in two and three space dimensions using a finite volume discretization on locally refined dyadic grids. Divergence cleaning is used to control…
Ideal magnetohydrodynamics (IMHD) is strongly constrained by an infinite number of microscopic constraints expressing mass, entropy and magnetic flux conservation in each infinitesimal fluid element, the latter preventing magnetic…
In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov-Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is…