@article{Rosswog2025, 
author = {Stephan Rosswog},
title = {Shock-Capturing Particle Hydrodynamics with Reproducing Kernels},
year = {2025},
journal = {Computer Modeling in Engineering & Sciences},
volume = {143},
number = {2},
pages = {1713-1741},
keywords = {Ideal hydrodynamics, reproducing kernels, shocks, instabilities, smoothed particle hydrodynamics},
url = {https://www.sciopen.com/article/10.32604/cmes.2025.062063},
doi = {10.32604/cmes.2025.062063},
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.}
}