Improving shock-capturing methods for relativistic hydrodynamics

Abstract Improving the accuracy of numerical modeling for relativistic simulations is a critical area of research. A key advancement in this field was the adaptation of modern high-resolution shock-capturing (HRSC) schemes, originally designed for non-relativistic flows, to incorporate relativistic effects. However, simply extending Newtonian HRSC schemes to relativistic flows has proven challenging. Several studies have shown that achieving grid-convergent numerical solutions often requires impractically fine grid resolutions. This persistent challenge demands further in-depth investigation. In this report, we share our latest progress in enhancing shock-capturing numerical methods for relativistic flows. We start by highlighting common numerical issues encountered when solving 1D shock-tube problems using existing HRSC approaches, especially when relativistic tangential velocities are present. To address these deficiencies, we introduce our new hybrid method. This approach significantly improves the simulation of relativistic shock-tube solutions, delivering sharply resolved shock and contact waves.