Boundary conditions for SPH through energy conservation

TL;DR

This paper presents a new energy-conserving boundary condition for SPH that enhances stability in wall boundary problems, demonstrated through various fluid dynamics scenarios.

Contribution

A novel boundary condition for SPH that prioritizes energy conservation, improving stability in wall boundary simulations.

Findings

Enhanced stability in SPH with the new boundary condition.

Successful application to diverse fluid dynamics problems.

Extension of SPH stability to wall boundary conditions.

Abstract

Dealing with boundary conditions in Smoothed Particle Hydrodynamics (SPH) poses significant difficulties, indeed being one of the SPHERIC Grand Challenges. In particular, wall boundary conditions have been pivotal in SPH model development since it evolved from astrophysics to more generic fluid dynamics simulations. Despite considerable attention from researchers and numerous publications dedicated to formulating and assessing wall boundary conditions, few of them have addressed the crucial aspect of energy conservation. This work introduces a novel boundary condition designed with energy conservation as a primary consideration, effectively extending the unconditional stability of SPH to problems involving wall boundary conditions. The result is formulated within the framework of the Boundary Integrals technique. The proposal is tested on a number of cases: normal impact against a wall, adiabatic oscillations of a piston, dam break, and the water landing of a spacecraft.