Analysis of an interior penalty DG method for the quad-curl problem

The quad-curl term is an essential part of the resistive magnetohydrodynamic equation and the fourth-order inverse electromagnetic scattering problem, which are both of great significance in science and engineering. It is desirable to develop efficient and practical numerical methods for the quad-curl problem. In this paper we first present some new regularity results for the quad-curl problem on Lipschitz polyhedron domains, and then propose a mixed finite element method for solving the quad-curl problem. With a novel discrete Sobolev imbedding inequality for the piecewise polynomials, we obtain stability results and derive error estimates based on a relatively low-regularity assumption of the exact solution.

On the Analytic Solution for a Steady Magnetohydrodynamic Equation

The purpose of this study is to apply the Laplace-Adomian Decomposition Method (LADM) for obtaining the analytical and numerical solutions of a nonlinear differential equation that describes a magnetohydrodynamic (MHD) flow near the forward stagnation point of two-dimensional and axisymmetric bodies. By using this method, the similarity solutions of the problem are obtained for some typical values of the model parameters. For getting computational solutions, we combined the obtained series solutions by LADM with the Padé approximation. The method is easy to apply and gives high accurate results. The presented results through tables and figures show the efficiency and accuracy of the proposed technique.

Optimal decay rate of classical solutions to the compressible magnetohydrodynamic equations

The three-dimensional compressible magnetohydrodynamic equation in the whole space are studied in this paper. The global classical solution is established when the initial data are small perturbations of some given constant state. Moreover, the optimal decay rate of the solution is also obtained.

LEVEL CROSSING ANALYSIS OF THE MAGNETOHYDRODYNAMIC EQUATION IN (1+1)-DIMENSION

In this paper we investigate the average frequency [Formula: see text] of a certain positive slope which is produced when the velocity and magnetic fields Vy and Bx are crossed by the level [Formula: see text] in the magnetohydrodynamic equation. This level crossing analysis is in the inviscid limit where υ→0 and of course before the appearance of the shocks. The main goal of this paper is to show that this quantity, [Formula: see text], is a good measure for the fluctuations of the velocity and magnetic fields in the magnetohydrodynamic turbulence.

Toroidal plasma configuration with anisotropic pressure

The relation between various surface quantities required in hydrodynamic calculations, and the relation between the parallel and perpendicular currents in an arbitrary magnetic toroidal plasma configuration with scalar pressure, are generalized to the case of anisotropic pressure. Magnetic co-ordinates for hydrodynamic equilibria in this configuration are defined. A general expression for the mean velocity of diffusion through a magnetic surface, on the basis of the one-fluid magnetohydrodynamic equation with anisotropic pressure, is derived.