Related papers: Conservative regularization of compressible dissip…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
A dynamical vectorial equation for homogeneous incompressible Hall-MHD turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results…
We have carried out high resolution MHD simulations of the nonlinear evolution of Kelvin-Helmholtz unstable flows in 2 1/2 dimensions. The modeled flows and fields were initially uniform except for a thin shear layer with a hyperbolic…
The Gratton-Vargas snowplow model, recently revisited and expanded (S K H Auluck, Physics of Plasmas, 20, 112501 (2013)), has given rise to significant new insights into some aspects of the Dense Plasma Focus (DPF), in spite of being a…
This paper deals with the optimal regularity for entropy solutions of conservation laws. For this purpose, we use two key ingredients: (a) fine structure of entropy solutions and (b) fractional $BV$ spaces. We show that optimality of the…
An analytical MHD model of a normal-polarity prominence with compressible flow is presented. The exact solution is constructed via a systematic nonlinear separation of variables method used to calculate several classes of MHD equilibria in…
We propose a system of conservation laws with relaxation source terms (i.e. balance laws) for non-isothermal viscoelastic flows of Maxwell fluids. The system is an extension of the polyconvex elastodynamics of hyperelastic bodies using…
The existence of global-in-time classical solutions to the Cauchy problem of compressible magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linear structure is a degenerated hyperbolic-parabolic…
We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
Various forms of exact laws governing magnetohydrodynamic (MHD) turbulence have been derived either in the incompressibility limit, or for isothermal compressible flows. Here we propose a more general method that allows us to obtain such…
It is found that the ideal magnetohydrodynamic equilibrium of an axisymmetric gravitating magnetically confined plasma with incompressible flows is governed by a second-order elliptic differential equation for the poloidal magnetic flux…
We investigate a compressible two-fluid Navier-Stokes type system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. We are…
Three-dimensional numerical simulations of decaying turbulence in a magnetized plasma are performed using a so-called FLR-Landau fluid model which incorporates linear Landau damping and finite Larmor radius (FLR) corrections. It is shown…
This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…
Exact solutions of the equation governing the equilibrium magetohydrodynamic states of an axisymmetric plasma with incompressible flows of arbitrary direction [H. Tasso and G.N.Throumoulopoulos, Phys. Pasmas {\bf 5}, 2378 (1998)] are…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have…
The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is extended to non-ideal relativistic plasmas in curved spacetime. The existence of generalized magnetofluid connections that are…
We generalize Tadmor's algebraic numerical flux condition for entropy-conservative discretizations of conservation laws to a broader class of secondary structures, i.e. possibly non-convex secondary quantities whose evolution can consist of…