A discontinuous shapeless particle method for the quasi-linear transport

Abstract

This paper considers a new version of the discontinuous particle method, whose higher accuracy is based on the “predictor-corrector” scheme. The peculiarity of this version is a new criterion of rearranging particles at the “corrector” stage. In contrast to the previously used version with the analysis of overlapping particles, which required an assumption about their form, we use another key characteristic of particles, namely, their mass, more precisely, the assumption that in the nonlinear elastic transport not only particle masses are conserved but also the mass located between the centers of these particles. This requirement leads to the fact that changing a distance between particles in the process of their movement and conservation of mass in the space between them, lead to a change in the density of one of the particles. A new version arose in the solution of the two-dimensional transport problems. We emphasize that the discontinuity is smeared into a single particle, which indicates to a high accuracy of the method. The construction of the method for a simple nonlinear transport problem is a necessary step to simulate the complex gas dynamics problems.