Context. At this time there does not exist a robust set of rules connecting low and high β waves across the β ≈ 1 layer. The work here contributes specifically to what happens when a low β fast wave crosses the β ≈ 1 layer and transforms into high β fast and slow waves. Aims. The nature of fast and slow magnetoacoustic waves is investigated in a finite β plasma in the neighbourhood of a twodime...

We are concerned with the approximation of undercompressive, regularizationsensitive, nonclassical solutions of hyperbolic systems of conservation laws by high-order accurate, conservative, and semidiscrete finite difference schemes. Nonclassical shock waves can be generated by diffusive and dispersive terms kept in balance. Particular attention is given here to a class of systems of conservati...

In the present work we derive and study a non-linear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However, we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite di...

This talk is dedicated to multi-dimensional numerical simulation of Euler equations for compressible flow problems. To fulfill the conditions of the Lax-Wendroff theorem, it is required that a numerical scheme conserves the mass, momentum and total energy. Associated with the consistency and the increase of the entropy, these conservation properties are sufficient, in 1D, to ensure that a conve...

We further investigate the high order positivity-preserving discontinuous Galerkin (DG) methods for linear hyperbolic and radiative transfer equations developed in [14]. The DG methods in [14] can maintain positivity and high order accuracy, but they rely both on the scaling limiter in [15] and a rotational limiter, the latter may alter cell averages of the unmodulated DG scheme, thereby affect...

The purpose of this paper is to develop a high-order shock-capturing scheme capable predicting flows where shock waves with high-temperature jumps interact multi-component real gas mixtures, assuming local thermodynamic equilibrium. We first propose generalization the Roe solver for distinct species non-ideal properties that relies on original method proposed by Vinokur & Montagné [1]. This use...

A stability theory is developed for dissipative difference approximations to multidimensional initial-boundary value problems. The original differential problem should be strictly hyperbolic and the difference problem consistent with the differential one. An algebra of pseudo-difference operators is built and later used to prove the stability of the difference approximation with variable coeffi...