Are heuristic switches necessary to control artificial viscosity in modern smoothed particle hydrodynamics ?

TL;DR

The paper tackles the challenge of dissipation control in SPH by proposing a switch-free AV scheme based on slope-limited velocity reconstruction (SLR) with a Balsara limiter. It demonstrates that AVSLR variants, particularly AVSLRB2, outperform traditional AV switches across shocks, shear flows, instabilities, and subsonic turbulence, while significantly reducing spurious dissipation in non-shock regions. A moderate AV-floor coupling (AVSLRB2F) further enhances turbulence resolution without sacrificing shock handling, suggesting near-optimal performance in a single framework. The findings advocate for adopting a switch-free, SLR-based AV with Balsara modulation as a robust, general-purpose approach in modern SPH codes, with potential refinements to adapt the floor to local flow properties.

Abstract

Artificial viscosity is commonly employed in Smoothed Particle Hydrodynamics (SPH) to model dissipation in hydrodynamic simulations. However, its practical implementation relies on complex numerical switches to restrict its application to regions where dissipation is physically warranted, such as shocks. These switches, while essential, are imperfect and can introduce additional numerical noise. In this work we develop and validate a more efficient artificial viscosity scheme for SPH that does not rely on heuristic switches. Recent studies have proposed that subtracting the linear component of the velocity field can suppress spurious dissipation in shear-dominated regions. Building on this idea, we implement a velocity-reconstruction technique that removes the bulk linear motion from the local velocity field and uses the Balsara correction to modulate the dissipation. The presented methodology yields a balanced dissipation scheme that performs well across a range of regimes, including subsonic instabilities, shear flows, and strong shocks. We demonstrate that this approach yields improved accuracy and lower spurious dissipation compared to conventional artificial viscosity switches

Figures (10)

• Figure 1: Velocity profile, $v_x$, for the shock-tube test and the models shown in the second row in Table \ref{['tab:table_cases']}, at time $t=0.2$
• Figure 2: Evolution of maximum density in the Sedov test for the different models described in Table \ref{['tab:table_cases']}.
• Figure 3: Density and radial velocity profiles in the Sedov-Taylor test at time $t=1$ for the different models described in Table \ref{['tab:table_cases']}. The solid line represents the analytical reference. The $L_1$ error between the numerical and analytical estimates from the center until the maximum radial velocity is also shown.
• Figure 4: Azimuthal velocity distribution in the Gresho-Chan vortex experiment at $t=1$ for models V$_k$ in the third row in Table \ref{['tab:table_cases']}. The analytical reference is indicated by the continuum line.
• Figure 5: Color-coded density for the KH models in Table \ref{['tab:table_cases']} at $t=3$ ($t/t_{\mathrm {KH}}=2.8$).