Open Access

ARTICLE

Shock-Capturing Particle Hydrodynamics with Reproducing Kernels

Stephan Rosswog^1,2,*

1 Hamburg Observatory, University of Hamburg, Gojenbergsweg 112, Hamburg, 21029, Germany
2 The Oskar Klein Centre, Department of Astronomy, AlbaNova, Stockholm University, Stockholm, 10691, Sweden

* Corresponding Author: Stephan Rosswog. Email:

Computer Modeling in Engineering & Sciences 2025, 143(2), 1713-1741. https://doi.org/10.32604/cmes.2025.062063

Received 09 December 2024; Accepted 28 April 2025; Issue published 30 May 2025

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.

---

Keywords

---