Special Relativistic Smoothed Particle Hydrodynamics Based on Riemann Solver

TL;DR

This paper introduces a new special relativistic SPH method using a Riemann solver to improve shock wave accuracy, conservation, and stability in high-resolution relativistic fluid simulations.

Contribution

It presents a novel relativistic SPH formulation based on Godunov methods with a Riemann solver, including new density calculation and variable smoothing length techniques.

Findings

Accurately simulates relativistic shock tube problems.

Effectively captures Kelvin-Helmholtz instabilities.

Demonstrates robustness and high resolution in tests.

Abstract

This paper proposes a novel numerical method based on Godunov Smoothed Particle Hydrodynamics for special relativistic fluid dynamics. Our method utilizes a Riemann solver to describe shock, enhancing accuracy in strong shock waves. The formulation maintains conservation laws and achieves higher accuracy through convolution integrals that define physical quantities for SPH particles. We also propose the number density calculation method that uses a non-equal baryon number in each SPH particle and variable smoothing length in a way different from the conventional method. Numerical experiments demonstrate the method's robustness across one- and two-dimensional relativistic shock tube problems, as well as its ability to simulate Kelvin-Helmholtz instabilities accurately, validating SRGSPH as a reliable approach for high-resolution relativistic simulations.