Building a Hydrodynamics Code with Kinetic Theory

TL;DR

This paper introduces a kinetic Monte Carlo code that combines methods to accurately simulate hydrodynamic systems across different density regimes, validated through shock wave tests relevant to astrophysics.

Contribution

The paper presents a novel hybrid kinetic Monte Carlo code that improves spatial accuracy and efficiency for simulating continuum matter in hydrodynamic regimes.

Findings

Successfully reproduces shock wave behavior in simulations

Maintains high spatial accuracy with large test-particle numbers

Applicable to astrophysical phenomena like supernovae

Abstract

We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the Point-of-Closest-Approach methods to solve the collision integral of the Boltzmann equation. With that, we achieve a high spatial accuracy in simulations while maintaining computational feasibility when applying a large number of test-particles. The hybrid setup of our approach allows us to study systems which move in and out of the hydrodynamic regime, with low and high particle densities. To demonstrate our code's ability to reproduce hydrodynamic behavior we perform shock wave simulations and focus here on the Sedov blast wave test. The blast wave problem describes the evolution of a spherical expanding shock front and is an important verification problem for codes which are applied in astrophysical simulation, especially for approaches which aim to study core-collapse supernovae.