New 3D Benchmark for CFD-Codes Based on Analytical Solution of Spherically-Symmetric Gas Free Expansion (Communications in Computational Physics, 2025)
The article presents for the first time the use of a known solution to theproblem of gas expansion into a vacuum as a test for the implementation of numericalmethods. An analytical solution of the problem of gas ball expanding into vacuum iswritten 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 sphericalsymmetry of a numerical solution when using a Cartesian or cylindrical coordinatesystem. Moreover, the actual order of approximation of an implemented numericalalgorithm, and the accuracy of reproducing the solution on a moving free boundarycan be estimated. We present the results of numerical solution of the problem by usingthree-dimensional Smoothed Particle Hydrodynamics (SPH) simulations. The simulation is performed for two methods of computing density in SPH. The algorithm forcomputing the dynamics of particles at gas-vacuum sharp interface is described in detail.