Visualization of the Application of the Discontinuous Shapeless Particle Method to the Problem of a Supersonic Flow Around a Wedge

Abstract

A modification of the discontinuous shapeless particle method for two-dimensional problems of gas dynamics is studied. In the previous version of the method, the shape of the particles conditioned their interaction, which determined the quality of the final result. In order to get rid of the constant attachment to the shape and size of particles, along with the heights of particles (solution of the differential problem) and their positions in space, another third invariant is introduced. Namely, the area of the trapezium, the bases of which are the heights of the particles, and the segment connecting their centers is the lateral side. This invariant can be interpreted as a trace of the conservation of mass in the space between two particles whose masses also do not change (exact conservatism is a fundamental feature of particle methods). Numerical solutions obtained with the particle method and numerical solutions obtained with the OpenFOAM software are compared with the analytical solution in the L2 norm, using the example of the problem of a supersonic flow around a wedge, resulting in the formation of an oblique shock wave. The presented visualization of the results gives a clear picture of the features of the discontinuous particle method for problems whose solution has large gradients. This work is part of the research on the comparative verification of numerical methods in the space of defining parameters.