TY  - EJOU
AU  - Rosswog, Stephan 

TI  - Shock-Capturing Particle Hydrodynamics with Reproducing Kernels
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2025
VL  - 143
IS  - 2
SN  - 1526-1506

AB  - 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.
KW  - Ideal hydrodynamics; reproducing kernels; shocks; instabilities; smoothed particle hydrodynamics

DO  - 10.32604/cmes.2025.062063