@Article{cmes.2025.062063,
AUTHOR = {Stephan Rosswog},
TITLE = {Shock-Capturing Particle Hydrodynamics with Reproducing Kernels},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {143},
YEAR = {2025},
NUMBER = {2},
PAGES = {1713--1741},
URL = {http://www.techscience.com/CMES/v143n2/61424},
ISSN = {1526-1506},
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.},
DOI = {10.32604/cmes.2025.062063}
}