An ADER-WENO Finite Volume AMR code for Astrophysics

TL;DR

This paper introduces a high-order ADER-WENO finite volume scheme with adaptive mesh refinement for astrophysical simulations, demonstrating improved accuracy and efficiency over traditional methods in complex hyperbolic systems.

Contribution

The paper presents a novel high-order one-step ADER-WENO scheme integrated with AMR, enhancing accuracy and computational efficiency for multidimensional astrophysical fluid dynamics.

Findings

The scheme outperforms traditional second-order AMR methods.

Successful tests on Euler and magnetohydrodynamics equations.

Demonstrated suitability for complex astrophysical scenarios.

Abstract

A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO reconstruction. Thanks to the one-step nature of the underlying scheme, the resulting algorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios.