In some previous works, the authors have introduced a strategy to develop well-balanced
high-order numerical methods for nonconservative hyperbolic systems in the framework of …

Computational fluid dynamics, commonly known by the acronym 'CFD', continues to have
significant expansion. There are many software packages available that solve fluid flow …

Well-balanced high-order finite volume schemes are designed to approximate the Euler
equations with gravitation. The schemes preserve discrete equilibria, corresponding to a …

A novel, simple, robust, and effective modification in the nonlinear weights of the scale-
invariant WENO operator is proposed that achieves an optimal order of accuracy with …

This work presents arbitrary high order well balanced finite volume schemes for the Euler
equations with a prescribed gravitational field. It is assumed that the desired equilibrium …

We develop a second-order well-balanced central-upwind scheme for the compressible
Euler equations with gravitational source term. Here, we advocate a new paradigm based …

The finite difference multi-resolution alternative weighted essentially non-oscillatory (MR-
AWENO) scheme has been designed to solve hyperbolic conservation laws (Wang et al. in …

Many interesting astrophysical and atmospheric problems involve flows near the hydrostatic
equilibrium state where the pressure gradient is balanced by the gravitational force. In this …

In this paper, we propose a fifth order well-balanced positivity-preserving finite difference
scale-invariant AWENO scheme for the compressible Euler equations with gravitational …

A high-order well-balanced scheme for the Euler equations with gravitation is presented.
The scheme is able to preserve a spatially high-order accurate discrete representation of …