A Random Choice SPH Scheme with Adaptive Viscosity

Classical smoothed particle hydrodynamics (SPH) method employs explicit artificial viscosity, which typically produce more dissipation than need, incorrectly smears contact discontinuities and overwhelms fluid turbulence. Several studies have proposed highly tuned versions of artificial viscosity, turning on and off near shocks or other troublesome wave features. A different scheme adapts Godunov\rq{}s idea of solving local Riemann problems as building blocks for SPH solver. However, these methods still introduce an effective numerical diffusion that can infect the entire numerical solution.
We propose a new SPH scheme that combines an approximate version of Glimm\rq{}s Random Choice method (RCM) with SPH. Our version approximately resolves hydrodynamic waves, and samples the approximate solution without explicit artificial viscosity. Several attractive features of this method is demonstrated by 1D shock tube tests. First, this method introduces adaptive artificial viscosity, assigning larger dissipation near discontinuities and smaller elsewhere. Secondly, it is less dissipative than classical SPH and GSPH resulting in less smearing of shock. Thirdly, this method also ameliorates pressure ``wiggle" around contact discontinuity.