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In this work, a consistent Smoothed Particle Hydrodynamics (SPH) model is proposed to deal with interfacial multiphase uid ows simulation. A Continuum Stress Surface formulation (CSS) [1] was developed in the framework of SPH method using a non-conservative rst order consistency operator to calculate the divergence of stress surface tensor. This enables the enhancement of the stability near the uid interface. This formulation benets of all the advantages of the one proposed by Adami et al [2] and, in addition, it can be applied to more than two phases uid ow simulations. The generalized wall boundary conditions [3] are modied in order to be well adapted to multiphase uid ows with dierent density and viscosity. A particle redistribution strategy is proposed R1: as an extension of the damping technique presented in [3] to adequately initialize the conditions of gravitational multiphase uid ows. This strategy is based on the gradual application of a damping technique to mitigate gravity force in both momentum and pressure wall boundary condition equations. Several computational tests are investigated to show the accuracy and convergence of the proposed SPH interfacial multiphase model. Moreover, a simulation of a rising bubble crossing two stratied uid layers is performed with more challenging constraints such as high density ratio, high viscosity ratio, and with presence of triple points

This paper develops a consistent particle method for capturing the highly non-linear behavior of violent free-surface flows, based on an Enhanced Weakly Compressible Moving Particle Semi-implicit (EWC-MPS) method. It pays special attention to the evaluation and improvement of two particle regularization techniques, namely, pairwise particle collision (PC) and particle shifting (PS). To improve the effectiveness of PC in removing noisy pressure field, and volume conservation issue of PS, we propose and evaluate several enhancements to these techniques, including a novel dynamic PC technique, and a consistent PS algorithm with new boundary treatments and additional terms (in the continuity and momentum equations).Besides, we introduce modified higher-order and anti-symmetric operators for the diffusive and shear force terms. Evaluation of the proposed developments for violent free-surface flow benchmark cases (2D dambreak, 3D water sloshing, and 3D dam-break with an obstacle) confirms an accurate prediction of the flow evolution and rigid body impact, as well as long-term stability of the simulations. The dynamic PC reduces pressure noises with low energy dissipation, and the consistent PS conserves the volume even for extreme deformations. Comparing the role of these new particle regularization techniques demonstrates the effectiveness of both in assuring the uniformity of the particle distribution and pressure fields; nevertheless, the implementation of PS is found to be more complex and time-consuming, mainly due to its need for free surface detection and boundary treatment with many tuning parameters.

In this work, a weakly compressible smoothed particle hydrodynamics (WC-SPH) multiphase model is developed. The model is able to deal with soilwater interactions coupled in a strong and natural form. A Regularized Bingham Plastic constitutive law including a pressure-dependent Mohr-Coulomb yield criterion (RBPMC-α µ ) is proposed to model fluids, soils and their interaction. Since the proposed rheology model is pressure-sensitive, we propose a multiphase diffusive term to reduce the spurious pressure resulting from the weakly compressible flow hypothesis. Several numerical benchmarks are investigated to assess the robustness and accuracy of the proposed multiphase SPH model.

In this work we present a δ-Smoothed Particle Hydrodynamics (SPH) scheme for weakly compressible flows with automatic adaptive numerical dissipation. The resulting scheme is a meshless self-adaptive method, in which the introduced artificial dissipation is designed to increase the dissipation in zones where the flow is under-resolved by the numerical scheme, and to decrease it where dissipation is not required. The accuracy and robustness of the proposed methodology is tested by solving several numerical examples. Using the proposed scheme, we are able to recover the theoretical decay of kinetic energy, even where the flow is under-resolved in very coarse particle discretizations. Moreover, compared with the original δ-SPH scheme, the proposed method reduces the number of problem-dependent parameters.

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In this work, we develop an enhanced particle shifting strategy in the framework of weakly compressible δ+-SPH method. This technique can be considered as an extension of the so-called improved particle shifting technology (IPST) proposed by Wang et al. (2019). We introduce a new parameter named “ϕ” to the particle shifting formulation, on the one hand to reduce the effect of truncated kernel support on the formulation near the free surface region, on the other hand, to deal with the problem of poor estimation of free surface particles. We define a simple criterion based on the estimation of particle concentration to limit the error’s accumulation in time caused by the shifting in order to achieve a long time violent free surface flows simulation. We propose also an efficient and simple concept for free surface particles detection. A validation of accuracy, stability and consistency of the presented model was shown via several challenging benchmarks.

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