Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations

The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic approximation in physical books. In this paper we justify this singular limit rigorously in the framework of smooth solutions for well-prepared initial data.Comment: 26page

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques

Fully Coupled Fluid and Electrodynamic Modeling of Plasmas: A Two-fluid Isomorphism and a Strong Conservative Flux-coupled Finite Volume Framework

Ideal and resistive magnetohydrodynamics (MHD) have long served as the incumbent framework for modeling plasmas of engineering interest. However, new applications, such as hypersonic flight and propulsion, plasma propulsion, plasma instability in engineering devices, charge separation effects and electromagnetic wave interaction effects may demand a higher-fidelity physical model. For these cases, the two-fluid plasma model or its limiting case of a single bulk fluid, which results in a single-fluid coupled system of the Navier-Stokes and Maxwell equations, is necessary and permits a deeper physical study than the MHD framework. At present, major challenges are imposed on solving these physical models both analytically and numerically. This dissertation alleviates these challenges by investigating new frameworks that facilitate efficient modeling of plasmas beyond the MHD description. Two investigations are performed: first, an isomorphism is constructed between the two-fluid plasma model and the Maxwell equations. This permits a set of unified Maxwell equations for both the electrodynamic and hydrodynamic behavior, but introduces an analogous notion of charge and current density for a fluid, which must be modeled to solve the new equations. We examine the homogeneous case (where these sources vanish), and then discuss iterative approaches and empirical modeling of the sources. We calculate some simple source models for fluid problems, including Blasius boundary layer flow. We demonstrate solution approaches using Green\u27s functions methods and the method of images, for which a closed-form solution to Blasius boundary layer flow is achieved. The second investigation recasts the single-fluid model into a strong conservative form. This permits the coupled Navier-Stokes and full Maxwell equations to be written exactly, but with no source terms present, which tend to cause numerical instability during simulation. The removal of the source terms is shown to improve the stability and robustness of the equations, but at the cost of introducing a significantly more complicated eigenstructure; we present the new eigenstructure for this system of equations and demonstrate an effective Riemann solver and flux splitting approach. Validation tests including magnetohydrodynamic problems, radio wave propagation tests and plasma instabilities and turbulence are presented

Global solutions to the three-dimensional full compressible magnetohydrodynamic flows

The equations of the three-dimensional viscous, compressible, and heat conducting magnetohydrodynamic flows are considered in a bounded domain. The viscosity coefficients and heat conductivity can depend on the temperature. A solution to the initial-boundary value problem is constructed through an approximation scheme and a weak convergence method. The existence of a global variational weak solution to the three-dimensional full magnetohydrodynamic equations with large data is established

Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows

The three-dimensional equations of compressible magnetohydrodynamic isentropic flows are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $\gamma>\frac32$ and constant viscosity coefficients