Shock-capturing particle hydrodynamics with reproducing kernels

TL;DR

This paper introduces a novel shock-capturing particle hydrodynamics method that combines reproducing kernels with Roe's Riemann solver and slope limiting, achieving high accuracy in complex 3D shock and instability simulations.

Contribution

The paper develops a new particle hydrodynamics approach using reproducing kernels and advanced Riemann solver techniques for improved shock capturing.

Findings

Accurate reproduction of constant and linear functions to machine precision.

Excellent agreement with analytical solutions in 3D shock and instability benchmarks.

Robust performance across a range of challenging fluid dynamics problems.

Abstract

We present and explore a new shock-capturing particle hydrodynamics approach. Our starting point is a commonly used discretization of smoothed particle hydrodynamics. We enhance this discretization with Roe's approximate Riemann solver, we identify its dissipative terms, and in these terms, we use slope-limited linear reconstruction. All gradients needed for our method are calculated with linearly reproducing kernels that are constructed to enforce the two lowest-order consistency relations. We scrutinize our reproducing kernel implementation carefully on a "glass-like" particle distribution, and we find that constant and linear functions are recovered to machine precision. We probe our method in a series of challenging 3D benchmark problems ranging from shocks over instabilities to Schulz-Rinne-type vorticity-creating shocks. All of our simulations show excellent agreement with analytic/reference solutions.