Incompressible δ-SPH via artificial compressibility

Smoothed particle hydrodynamics using artificial compressibility (ACSPH) is developed, with the inclusion of pressure smoothing terms. Theoretical links between pressure/velocity correction incompressible SPH and artificial compressibility are explored, illustrating that ACSPH may be considered an extension of, or closely related to, the 𝛿-SPH method. An implicit dual-time integration procedure is used to enforce an incompressible solution at every time-step, removing acoustic effects arising from the common assumption of weak compressibility. An established weakly-compressible quasi-Lagrangian 𝛿-SPH method is used for comparison against ACSPH, and a series of test cases show that ACSPH provides a similar solution cost to 𝛿-SPH. However, the residual acoustic effects in 𝛿-SPH are removed entirely in ACSPH, providing improved pressure prediction capabilities across all test cases, including intense fluid impacts. Improved modelling of fluid-structure-interaction cases and coupled energy dissipation are also recorded as a result of correctly capturing incompressible flow.