Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR(Adaptive-Mesh Refinement) and Results From Special and General Relativistic Hydrodynamic

TL;DR

This paper presents a comprehensive method for solving three-dimensional general relativistic hydrodynamics equations using adaptive mesh refinement, demonstrating improved accuracy and efficiency through various tests in special and general relativity contexts.

Contribution

It introduces a new procedure combining AMR with HRSC schemes for 3D GRH equations, verified by multiple test problems and convergence analysis.

Findings

AMR improves resolution efficiency over uniform grids.

The code achieves second-order convergence in 1D, 2D, and 3D.

Coupling flux and source terms yields accurate solutions.

Abstract

In this paper, the general procedure to solve the General Relativistic Hydrodynamical(GRH) equations with Adaptive-Mesh Refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of general relativistic hydrodynamic equations are done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second order convergence of the code in 1D, 2D and 3D. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the general relativistic hydrodynamical equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.