TESS: A Relativistic Hydrodynamics Code on a Moving Voronoi Mesh

TL;DR

TESS is a versatile relativistic hydrodynamics code utilizing a dynamic Voronoi mesh that adapts to fluid motion, offering high accuracy and reduced diffusion in astrophysical simulations.

Contribution

The paper introduces TESS, a novel hydrodynamics code that employs a moving Voronoi mesh for improved accuracy in relativistic and non-relativistic fluid simulations.

Findings

TESS reduces numerical diffusion compared to fixed mesh codes.

It accurately captures contact discontinuities and shock waves.

The code is adaptable to various coordinate systems and physics modules.

Abstract

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multi-dimensional systems of conservation laws in finite-volume form. The mesh generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluids on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical and cylindrical coordinates and is modular so that auxilliary physics solvers are readily integrated into the TESS framework and so that the TESS framework can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.