(untitled) (Communications in Computational Physics, 2025)
The article presents for the first time the use of a known solution to the problem of gas expansion into a vacuum as a test for the implementation of numerical methods. An analytical solution of the problem of gas ball expanding into vacuum is written out in an explicit form. The solution is designed for benchmarking of three-dimensional gas dynamics solvers. The test makes it possible to evaluate a spherical symmetry of a numerical solution when using a Cartesian or cylindrical coordinate system. Moreover, the actual order of approximation of an implemented numerical algorithm, and the accuracy of reproducing the solution on a moving free boundary can be estimated. We present the results of numerical solution of the problem by using three-dimensional Smoothed Particle Hydrodynamics (SPH) simulations. The simulation is performed for two methods of computing density in SPH. The algorithm for computing the dynamics of particles at gas-vacuum sharp interface is described in detail.