A weakly compressible SPH method for violent multi-phase flows with high density ratio

Abstract

The weakly compressible SPH (WCSPH) method is known suffering from low computational efficiency, or unnatural voids and unrealistic phase separation when it is applied to simulate highly violent multi-phase flows with high density ratio, such as that between water and air. In this paper, to remedy these issues, we propose a multi-phase WCSPH method based on a low-dissipation Riemann solver and the transport-velocity formulation. The two-phase Riemann problem is first constructed to handle the pairwise interaction between fluid particles, then modified for the fluid-wall interaction to impose the solid wall boundary condition. Since the method uses the same artificial speed of sound for both heavy and light phases, the computational efficiency increases greatly. Furthermore, due to the transport-velocity formulation employed for the light phase and application of the two-phase Riemann problem, the unnatural voids and unrealistic phase separation are effectively eliminated. The method is validated with several 2-and 3D cases involving violent water-air flows. The results have been compared with existing experimental data, previous numerical and analytical solutions, where the proposed method demonstrates good robustness, improved or comparable accuracy, respectively, comparing to previous methods with same choice of sound speed or those with much less computational efficiency.

A WCSPH Particle Shifting Strategy for Simulating Violent Free Surface Flows

“…A perfect agreement is shown between both numerical approaches since at this stage the accumulated errors due to the use of particle shifting is not significant (non-expansion is observed during all the time presented in Figure 24, in other words, C i > 0.98 everywhere in the inner particles). As a quantitative comparison, the numerical results correspond relatively to the analytical solution from shallow water theory [76], and experimental data given by Buchner [69], however, it should be noted that a slower front wave is observed in experiments caused by several factors such as uncertainties of the measurements and wall roughness [77]. .00, 14.80, 20.03}, The left column depicts the results obtained by the present method.…”

“…When the frequency of the tank motion is close to the natural frequency of the fluid due to gravitational wave, the resonance conditions prevail and may cause important loads impacts to the tank structures. Because this phenomenon is of complex and highly non-linear nature, the liquid sloshing flow has been used in several works to validate SPH models [77,[80][81][82].…”

Enhanced weakly-compressible MPS method for violent free-surface flows: Role of particle regularization techniques

“…This benchmark case has been the focus of numerous particle methods (e.g., [8,9,29,54]). Capturing these complex flows, dominated by water-water and water-solid impacts, requires robust particle regularization techniques to eliminate possible numerical instabilities while conserving the total momentum and energy of the system [5].…”

“…For this purpose, in addition to employing higher-order formulations and diffusive terms, eliminating the particlepairing instabilities requires rigorous particle regularization techniques [5]. The PS techniques (e.g., [36,38]), transport-velocity algorithms (e.g., [29,39]), and the PC method (e.g., [21,22]) have been specifically developed and utilized to surmount the numerical instability of violent free-surface flows.…”

Improved δ-SPH Scheme with Automatic and Adaptive Numerical Dissipation

“…A quantitative agreement with the experimental data is also observed, although it should be noted that a slower front wave is observed in the experiments. This could be caused by several factors such as uncertainties of the measurements and wall roughness, as exposed in [59]. Figure 15 (right) shows a comparison of the time evolution of the pressure signals at the probe between the proposed method and the δ-LES-SPH for H/∆x 0 = 80.…”