MPS mesh-free particle method for multiphase flows

By treating the multiphase system as a multi-density multi-viscosity fluid, a straightforward model has been proposed in this paper based on the Moving Particle Semi-implicit (MPS) mesh-free particle method for incompressible multiphase flow. The weakly-compressible MPS (WC-MPS) formulation (developed by the authors) is used to solve a single set of equations for all of the phases. In the model, the multiphase forces are introduced in a straightforward way. Dealing with multi-viscosity systems, different methods for defining the viscosity, by which particles of different phases interact, is examined. To evaluate the accuracy of each of these methods, a stratified multi-viscosity Poiseuille flow test case is used and model results are compared with the analytical solution. The results show that selection of this interaction viscosity has an important role in the accuracy of the results. The model is then validated and applied to two basic hydrodynamic instability cases (Rayleigh–Taylor and Kelvin–Helmholtz instabilities). The results are then compared to a mesh-based model (with volume of fluid interface tracing method) to examine the ability of the model to deal with the multi-density systems. Comparisons show the model has reasonable accuracy. The results of this work offer the potential of modeling of multiphase incompressible immiscible systems in an extensive range of conditions using MPS.

[1]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[2]  T. Schwager,et al.  Computational Granular Dynamics: Models and Algorithms , 2005 .

[3]  Hitoshi Gotoh,et al.  Lagrangian Two-Phase Flow Model of the Settling Behavior of Fine Sediment Dumped into Water , 2001 .

[4]  J. Brackbill,et al.  A continuum method for modeling surface tension , 1992 .

[5]  J. Monaghan.  Simulating Free Surface Flows with SPH , 1994 .

[6]  Abbas Khayyer,et al.  Modified Moving Particle Semi-implicit methods for the prediction of 2D wave impact pressure , 2009 .

[7]  Piet D. Iedema,et al.  Modelling multi-viscosity systems with dissipative particle dynamics , 2006, J. Comput. Phys..

[8]  Benedict D. Rogers,et al.  Numerical Modeling of Water Waves with the SPH Method , 2006 .

[9]  Daniel J. Price.  Modelling discontinuities and Kelvin-Helmholtz instabilities in SPH , 2007, J. Comput. Phys..

[10]  L. Lucy.  A numerical approach to the testing of the fission hypothesis. , 1977 .

[11]  George Keith Batchelor,et al.  An Introduction to Fluid Dynamics. , 1969 .

[12]  Ajay K. Prasad,et al.  Direct numerical simulations of two-layer viscosity-stratified flow , 2004 .

[13]  Yoshiaki Oka,et al.  Numerical Analysis of Droplet Breakup Behavior using Particle Method , 2001 .

[14]  J. Morris,et al.  Modeling Low Reynolds Number Incompressible Flows Using SPH , 1997 .

[15]  Nikolaus A. Adams,et al.  A multi-phase SPH method for macroscopic and mesoscopic flows , 2006, J. Comput. Phys..

[16]  Yee-Chung Jin,et al.  A weakly compressible MPS method for modeling of open‐boundary free‐surface flow , 2009 .

[17]  Joseph J Monaghan,et al.  An introduction to SPH , 1987 .

[18]  S. Koshizuka,et al.  International Journal for Numerical Methods in Fluids Numerical Analysis of Breaking Waves Using the Moving Particle Semi-implicit Method , 2022 .

[19]  Yee-Chung Jin,et al.  MPS-Based Mesh-Free Particle Method for Modeling Open-Channel Flows , 2011 .

[20]  J. Koelman,et al.  Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics , 1992 .

[21]  Yoshiaki Oka,et al.  A hybrid particle-mesh method for viscous, incompressible, multiphase flows , 2005 .

[22]  J. Monaghan,et al.  Smoothed particle hydrodynamics: Theory and application to non-spherical stars , 1977 .

[23]  J. Monaghan.  On the problem of penetration in particle methods , 1989 .

[24]  S. Koshizuka,et al.  Moving-Particle Semi-Implicit Method for Fragmentation of Incompressible Fluid , 1996 .

[25]  Hitoshi Gotoh,et al.  Sub-particle-scale turbulence model for the MPS method , 2001 .

[26]  J. Monaghan,et al.  Fundamental differences between SPH and grid methods , 2006, astro-ph/0610051.

[27]  David Le Touzé,et al.  An Hamiltonian interface SPH formulation for multi-fluid and free surface flows , 2009, J. Comput. Phys..

[28]  C. W. Hirt,et al.  Volume of fluid (VOF) method for the dynamics of free boundaries , 1981 .

[29]  Nikolaus A. Adams,et al.  A new surface-tension formulation for multi-phase SPH using a reproducing divergence approximation , 2010, J. Comput. Phys..

[30]  S. Koshizuka.  A particle method for incompressible viscous flow with fluid fragmentation , 1995 .

[31]  J. Monaghan,et al.  SPH simulation of multi-phase flow , 1995 .