SPHS: smoothed particle hydrodynamics with a higher order dissipation switch

Abstract

We present a novel implementation of smoothed particle hydrodynamics that uses the spatial derivative of the velocity divergence as a higher order dissipation switch. Our switch – which is second order accurate – detects flow convergence before it occurs. If particle trajectories are going to cross, we switch on the usual SPH artificial viscosity, as well as conservative dissipation in all advected fluid quantities (e.g. the entropy). The viscosity and dissipation terms (that are numerical errors) are designed to ensure that all fluid quantities remain single valued as particles approach one another, to respect conservation laws, and to vanish on a given physical scale as the resolution is increased. SPHS alleviates a number of known problems with ‘classic’ SPH, successfully resolving mixing, and recovering numerical convergence with increasing resolution. An additional key advantage is that – treating the particle mass similarly to the entropy – we are able to use multimass particles, giving significantly improved control over the refinement strategy. We present a wide range of code tests including the Sod shock tube, Sedov–Taylor blast wave, Kelvin–Helmholtz Instability, the ‘blob test’ and some convergence tests. Our method performs well on all tests, giving good agreement with analytic expectations.

Improved Performances in Subsonic Flows of an SPH Scheme With Gradients Estimated Using an Integral Approach

“…For the Gresho-Chan vortex problem it is well known (Read & Hayfield 2012;Dehnen & Aly 2012;Hu et al 2014;Hopkins 2015) that standard SPH is heavily affected by the E 0 error and the code performances are very poor. On the contrary, the IA formulation leads to much better behavior, with the results of Section 4.1 being in line with those obtained by other numerical schemes (Springel 2010;Hopkins 2015).…”

“…For the Gresho-Chan vortex test the convergence rate has already been estimated for a variety of different SPH implementations, so that Figure 3 can be compared with the corresponding rates already obtained by various authors (Dehnen & Aly 2012;Read & Hayfield 2012;Hu et al 2014;Rosswog 2015;Zhu et al 2015).…”

“…It is then particularly problematic for standard SPH to successfully model this problem leaving unaltered the velocity profile during the simulation, and in the literature (Springel 2010;Dehnen & Aly 2012;Read & Hayfield 2012;Kawata et al 2014;Hu et al 2014;Hopkins 2015;Rosswog 2015;Zhu et al 2015) it has been widely used to validate code performances.…”

“…Finally, other variants of SPH are based on Riemann solvers (Godunov-SPH: Inutsuka 2002;Cha et al 2010;Murante et al 2011), Voronoi tessellation techniques (Heß & Springel 2010) or on the use of high order dissipation switches (Read & Hayfield 2012).…”

Godunov SPH with an operator-splitting procedure for materials with strength

“…This may be achieved by a time-consuming trialand-error analysis [15] which may be very undesirable for the user. The special treatments mentioned rely on using higher-order terms [14,2] to detect shock-indicative flow convergence before it occurs or an estimation of the vorticity to minimize damping in regions of pure shear [1] so locally varying damping can be applied more optimally. While these treatments reduce the undesirable effects of the AV, they still require user-defined damping parameters which, in some cases such as hypervelocity impacts, may provide insufficient damping and cause numerical oscillations to destroy the solution.…”