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Conservative numerical methods for a two-temperature resistive MHD model with self-generated magnetic field term

Marc Wolff, Stéphane Jaouen, Lise-Marie Imbert-Gérard (2011)

ESAIM: Proceedings

We propose numerical methods on Cartesian meshes for solving the 2-D axisymmetric two-temperature resistivive magnetohydrodynamics equations with self-generated magnetic field and Braginskii’s [1] closures. These rely on a splitting of the complete system in several subsystems according to the nature of the underlying mathematical operator. The hyperbolic part is solved using conservative high-order dimensionally split Lagrange-remap schemes whereas...

Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

Nicolas Besse, Dietmar Kröner (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition Δ t h 4 / 3 , we obtain error estimates in L 2 of order 𝒪 ( Δ t 2 + h m + 1 / 2 ) where m is the degree of the local polynomials.

Convergence of locally divergence-free discontinuous-Galerkin methods for the induction equations of the 2D-MHD system

Nicolas Besse, Dietmar Kröner (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present the convergence analysis of locally divergence-free discontinuous Galerkin methods for the induction equations which appear in the ideal magnetohydrodynamic system. When we use a second order Runge Kutta time discretization, under the CFL condition Δ t h 4 / 3 , we obtain error estimates in L2 of order 𝒪 ( Δ t 2 + h m + 1 / 2 ) where m is the degree of the local polynomials.

Convergent finite element discretizations of the nonstationary incompressible magnetohydrodynamics system

Andreas Prohl (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The incompressible MHD equations couple Navier-Stokes equations with Maxwell's equations to describe the flow of a viscous, incompressible, and electrically conducting fluid in a Lipschitz domain Ω 3 . We verify convergence of iterates of different coupling and decoupling fully discrete schemes towards weak solutions for vanishing discretization parameters. Optimal first order of convergence is shown in the presence of strong solutions for a splitting scheme which decouples the computation of velocity...

Directional and scale-dependent statistics of quasi-static magnetohydrodynamic turbulence

Naoya Okamoto, Katsunori Yoshimatsu, Kai Schneider, Marie Farge (2011)

ESAIM: Proceedings

Anisotropy and intermittency of quasi-static magnetohydrodynamic (MHD) turbulence in an imposed magnetic field are examined, using three-dimensional orthonormal wavelet analysis. Wavelets are an efficient tool to examine directional scale-dependent statistics, since they are based on well-localized functions in space, scale and direction. The analysis is applied to two turbulent MHD flows computed by direct numerical simulation with 5123 grid points...

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