Efficient implementation of the hybrid large-particle method

Within the framework of the hybrid large-particle method, an efficient algorithm with controlled numerical dissipation of the second order of accuracy in space and time is proposed. The computational properties of the algorithm were tested on one-dimensional Einfeldt, Tang or Liu, LeBlanc, Shu and Osher test problems, as well as two-dimensional Riemann problems. The algorithm demonstrated robustness and high resolution comparable to modern schemes having a formally higher order of approximation.