As computational astrophysics comes under pressure to become a precision science, there
is an increasing need to move to high accuracy schemes for computational astrophysics …

In this article, we present a multi-dimensional-aware Eulerian Riemann Solver (RS) and its
associated Finite Volume (FV) scheme for the 2D Shallow-Water (SW) equations. This RS …

Since being proposed, the HLLEM-type schemes have been widely used because they are
with high discontinuity resolutions and can be easily applied to the other system of …

We present a new numerical model for solving the Chew–Goldberger–Low system of
equations describing a bi-Maxwellian plasma in a magnetic field. Heliospheric and …

We propose a numerical dissipation switch, which helps to control the amount of numerical
dissipation present in central-upwind schemes. Our main goal is to reduce the numerical …

The constrained transport (CT) method reflects the state of the art numerical technique for
preserving the divergence-free condition of magnetic field to machine accuracy in multi …

This paper deals with a class of efficient, genuinely two-dimensional Riemann solvers for
hyperbolic nonconservative systems. A particularity of these solvers is that only a bound on …

A genuinely two-dimension Riemann solver for compressible flows in curvilinear
coordinates is proposed. Following Balsara's idea, this two-dimension solver considers not …

The high-accuracy solution of the MHD equations is of great interest in various fields of
physics, mathematics, and engineering. Higher-order DG schemes offer low dissipation and …

A high-order finite difference numerical scheme is developed for the ideal
magnetohydrodynamic equations based on an alternative flux formulation of the weighted …