In modelling incompressible flows using the Smoothed Particle Hydrodynamics method (SPH), an equation of state with a large sound speed is typically used. This weakly compressible approach (WCSPH), results in a stiff set of equations with a noisy pressure field and stability issues at high Reynolds number. As a remedy, an incompressible SPH technique was introduced  (ISPH), which uses a pressure projection technique to model incompressibility. In this paper, the incompressible and weakly compressible forms of the SPH method are employed to study sloshing flow. Both methods are compared with experimental data. The results show the incompressible SPH method provides more accurate pressure fields and free-surface profiles when compared to experiment.
The Effect of Pressure Solution in SPH Simulations of Sloshing Flow
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Rafiee, A, Cummins, S, Rudman, M, & Thiagarajan, K. "The Effect of Pressure Solution in SPH Simulations of Sloshing Flow." Proceedings of the ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. Volume 6: Ocean Engineering. Rotterdam, The Netherlands. June 19–24, 2011. pp. 129-138. ASME. https://doi.org/10.1115/OMAE2011-49215
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