Numerically solving partial differential equations (PDEs) can be challenging and
computationally expensive. This has led to the development of reduced-order models …

In this paper we develop a new well-balanced discontinuous Galerkin (DG) finite element
scheme with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler …

We introduce a general framework for the construction of well-balanced finite volume
methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense …

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 …

We herein present a novel methodology to construct very high order well-balanced schemes
for the computation of the Euler equations with gravitational source term, with application to …

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 …

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 …

Euler equations with gravitational source terms are used to model many astrophysical and
atmospheric phenomena. This system admits hydrostatic balance where the flux produced …

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 …

This paper presents novel high-order accurate discontinuous Galerkin (DG) schemes for the
compressible Euler equations under gravitational fields. A notable feature of these schemes …