Embedment of WENO-Z reconstruction in Lagrangian WLS scheme implemented on GPU for strongly-compressible multi-phase flows

It is a notoriously challenge problem for Lagrangian particle methods to solve compressible flows with strong discontinuities and large volume variations. To overcome the problems of numerical oscillations, an accurate and stable Lagrangian Weighted-Least-Square (LWLS) method embedded with WENO-Z scheme (LWLS-WENO-Z) is proposed. To further enhance the numerical accuracy and stability, the particle shifting technique, the multi-level local-refinement technique, and the interface repulsive force are appropriately employed in the numerical scheme. Moreover, the smooth and stable coupled particle method between the LWLS and Roe's Riemann solver (LWLSRR) is considered for the comparisons, further demonstrating the merit of the proposed LWLSWENO-Z scheme. To reduce the simulation time, parallel computing with a CUDA-based program for the proposed scheme is implemented on a single GPU. In the numerical experiments, several 1D/2D benchmarks are solved to test the accuracy of the proposed method. Particularly, the challenge 2D underwater explosion and the cavitation bubble collapse and jetting are numerically investigated. Compared to other reference solutions, the present coupled particle method demonstrates robustness and superior accuracy in simulating these strongly-compressible multi-phase flows.