Differential Geometrically Consistent Artificial Viscosity in Comoving Curvilinear Coordinates

TL;DR

This paper introduces a geometrically consistent artificial viscosity tensor tailored for comoving, curvilinear coordinate grids in high-resolution astrophysical simulations, ensuring better numerical accuracy.

Contribution

It proposes a modified tensor of artificial viscosity that is compatible with generally comoving, curvilinear grids, extending previous methods.

Findings

The isotropic part of the artificial viscosity tensor must be metrically modified in curvilinear coordinates.

The new tensor maintains desired properties in comoving, curvilinear coordinate systems.

Analytical comparison shows improved consistency over previous implementations.

Abstract

Context. High-resolution numerical methods have been developed for nonlinear, discontinuous problems as they appear in simulations of astrophysical objects. One of the strategies applied is the concept of artificial viscosity. Aims. Grid-based numerical simulations ideally utilize problem-oriented grids in order to minimize the necessary number of cells at a given (desired) spatial resolution. We want to propose a modified tensor of artificial viscosity which is employable for generally comoving, curvilinear grids. Methods. We study a differential geometrically consistent artificial viscosity analytically and visualize a comparison of our result to previous implementations by applying it to a simple self-similar velocity field. We give a general introduction to artificial viscosity first and motivate its application in numerical analysis. Then we present how a tensor of artificial viscosity has to be designed when going beyond common static Eulerian or Lagrangian comoving rectangular grids. Results. We find that in comoving, curvilinear coordinates the isotropic (pressure) part of the tensor of artificial viscosity has to be modified metrically in order for it to fulfill all its desired properties.