The moving particle semi-implicit (MPS) method is extended into a multiphase MPS (MMPS) method, where multiphase fluids are modeled as a multi-viscosity and multi-density fluid. Interparticle viscosity and density are adopted to model the interaction between particles of different phases. However, such a straightforward extension is prone to instability because the light particles at the interface suffer from exceptionally high acceleration. Therefore, two approaches, MMPS-HD (harmonic density) and MMPS-CA (continuous acceleration), are proposed to suppress the instability. In the first approach, harmonic mean interparticle density is applied to discretize the multiphase pressure Poisson equation to avoid the exceptionally high acceleration at the interface. In the second approach, new MMPS formulations are derived from the locally weighted average of interaction acceleration between particles to guarantee the continuity of acceleration and velocity. The particle

Numerical simulation of free surface multi-fluid flow is a challenging problem owning to the interaction between deformed interface and free surface. In this paper, a multiphase particle solver (free surface multiphase moving particle semi-implicit method, FS-MMPS) is developed to predict the early spreading flow of spilled oil where exist the oil-water interface and air-oil/air-water free surface. First, a multiphase virtual particle model is proposed to substitute the inaccurate free surface boundary condition for multiphase flow in conventional MPS methods. Specifically, virtual particles of different liquid phases are compensated outside free surface so that the pressure of free surface particles can be solved from pressure Poisson equation, thereby improving the accuracy of multi-fluid interaction at free surface. Meanwhile, a pressure gradient model based on the coupling of Taylor series expansion and dynamic specification of particle stabilizing term (PST) is proposed to simultaneously enhance accuracy and depress instability caused by multiphase virtual particles. Experiments of early spreading of thick oil slicks and continuous oil spill from a damaged tank are conducted for validation and demonstration of the accuracy and

Summary The Lagrangian moving particle semi‐implicit (MPS) method has potential to simulate free‐surface and multiphase flows. However, the chaotic distribution of particles can decrease accuracy and reliability in the conventional MPS method. In this study, a new Laplacian model is proposed by removing the errors associated with first‐order partial derivatives based on a corrected matrix. Therefore, a corrective matrix is applied to all the MPS discretization models to enhance computational accuracy. Then, the developed corrected models are coupled into our previous multiphase MPS methods. Separate stabilizing strategies are developed for internal and free‐surface particles. Specifically, particle shifting is applied to internal particles. Meanwhile, a conservative pressure gradient model and a modified optimized particle shifting scheme are applied to free‐surface particles to produce the required adjustments in surface normal and tangent directions, respectively. The simulations of a multifluid pressure oscillation flow and a bubble rising flow demonstrate the accuracy improvements of the corrective matrix. The elliptical drop deformation demonstrates the stability/accuracy improvement of the present stabilizing strategies at free surface. Finally, a turbulent multiphase flow with complicated interface fragmentation and coalescence is simulated to demonstrate the capability of the developed method.

No abstract

No abstract

No abstract

No abstract

Viscosity is an important property of fluids but it is not easy to simulate, especially for flows where viscous forces are dominant or comparable with other forces, because numerical viscosity may interfere. The paper mainly discusses the effect of setting up time step and space step on the stability and accuracy of the viscosity term in the moving particle semi-implicit (MPS) method. Two principles, the stability condition of the viscosity term and the accuracy condition of the viscosity term, are proposed for setting up time step and space step. The former can guarantee the stability of the viscous simulation by introducing extra numerical viscosity and the latter can produce a realistic and accurate simulation of the viscosity term without numerical viscosity interference. The simulated results for Poiseuille flow show that the simulation cases set up according to the stability condition of the viscosity term are stable and that the simulation cases set up according to the accuracy condition of the viscosity term are the most accurate. The proposed conditions can guide one to stable and accurate simulation for viscous flow by the MPS method.