Explicit incompressible SPH algorithm for free-surface flow modelling: A comparison with weakly compressible schemes

Several numerical schemes are available to simulate fluid flow with Smoothed Particles Hydrodynamics (SPH). Although commonly experiencing pressure fluctuations, schemes allowing for small changes in fluid density, referred to as weakly compressible (WCSPH and δ-SPH), are often used because of their faster computational time when compared to implicit incompressible schemes (IISPH). Explicit numerical schemes for incompressible fluid flow (EISPH), although more computationally efficient than IISPH, have not been largely used in the literature. To explore advantages and disadvantages of EISPH, this study compared an EISPH scheme with WCSPH and δ-SPH. The three schemes were compared for the case of still water and a wave generated by a dam-break. EISPH and δ-SPH were also compared for the case of a dam-break wave colliding with a vertical wall and a dam-break wave flowing over a wet bed. The three schemes performed similarly in reproducing theoretical and experimental results. EISPH led to results overall similar to WCSPH and δ-SPH, but with smoother pressure dynamics and faster computational times. EISPH presented some errors in the imposition of incompressibility, with the divergence of velocity being different from zero in parts of the fluid flow, especially near the surface. These errors in the divergence of velocity were comparable to the values of velocity divergence obtained with δ-SPH. In an attempt to reduce the velocity divergence in EISPH, an iterative procedure was implemented to calculate the pressure (iterative-EISPH). Although no real improvement was achieved in terms of velocity divergence, the pressure thus calculated was smoother and in some cases was closer to measured experimental values.