Dual-criteria time stepping for weakly compressible smoothed particle hydrodynamics

Implementing particle-interaction configuration and time integration are performance intensive essentials of particle-based methods. In this paper, a dual-criteria time-stepping method is proposed to improve the computational efficiency of the weakly-compressible smoothed particle hydrodynamic (WCSPH) method for modeling incompressible flows. The key idea is to introduce an advection time criterion, which is based on fluid velocity field, for recreating the particle-interaction configuration. Within this time criterion, several steps of pressure relaxation determined by the acoustic time criterion, based on the artificial speed of sound, can be carried out without updating the particle interaction configuration and much larger time-step sizes compared with the conventional counterpart. The method has shown optimized computational performance through CPU cost analysis. Good accuracy and performance is obtained for the presented benchmarks implying promising potential of the proposed method for incompressible flow and fluid-structure interaction simulations.

[1]  Moncho Gómez-Gesteira,et al.  Neighbour lists in smoothed particle hydrodynamics , 2011 .

[2]  Daniel Winkler,et al.  Neighbour lists for smoothed particle hydrodynamics on GPUs , 2017, Comput. Phys. Commun..

[3]  A. Colagrossi,et al.  Extension of the δ-Plus-SPH model for simulating Vortex-Induced-Vibration problems , 2019, Journal of Fluids and Structures.

[4]  Mostafa Safdari Shadloo,et al.  Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges , 2016 .

[5]  Michael Dumbser,et al.  A new 3D parallel SPH scheme for free surface flows , 2009 .

[6]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[7]  Nikolaus A. Adams,et al.  A splitting scheme for highly dissipative smoothed particle dynamics , 2010, J. Comput. Phys..

[8]  Salvatore Marrone,et al.  A dynamic δ-SPH model: How to get rid of diffusive parameter tuning , 2019, Computers & Fluids.

[9]  V. Springel.  The Cosmological simulation code GADGET-2 , 2005, astro-ph/0505010.

[10]  J. Monaghan,et al.  Shock simulation by the particle method SPH , 1983 .

[11]  Nikolaus A. Adams,et al.  A transport-velocity formulation for smoothed particle hydrodynamics , 2013, J. Comput. Phys..

[12]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[13]  Rade Vignjevic,et al.  SPH in a Total Lagrangian Formalism , 2006 .

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

[15]  D. Graham,et al.  Simulation of wave overtopping by an incompressible SPH model , 2006 .

[16]  Nikolaus A. Adams,et al.  A weakly compressible SPH method with WENO reconstruction , 2019, J. Comput. Phys..

[17]  Krish Thiagarajan,et al.  Study of liquid sloshing: numerical and experimental approach , 2011 .

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

[19]  A. Colagrossi,et al.  δ-SPH model for simulating violent impact flows , 2011 .

[20]  Taro Arikawa,et al.  On enhancement of Incompressible SPH method for simulation of violent sloshing flows , 2014 .

[21]  B. Rogers,et al.  GPUs, a New Tool of Acceleration in CFD: Efficiency and Reliability on Smoothed Particle Hydrodynamics Methods , 2011, PloS one.

[22]  S. Turek,et al.  Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow , 2006 .

[23]  W. Benz,et al.  Simulations of brittle solids using smooth particle hydrodynamics , 1995 .

[24]  Mikito Furuichi,et al.  Computational performance of a smoothed particle hydrodynamics simulation for shared-memory parallel computing , 2015, Comput. Phys. Commun..

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

[26]  Abbas Khayyer,et al.  On the state-of-the-art of particle methods for coastal and ocean engineering , 2018 .

[27]  Robert A. Dalrymple,et al.  Three-dimensional reversed horseshoe vortex structures under broken solitary waves , 2014 .

[28]  Kazem Hejranfar,et al.  A truly incompressible smoothed particle hydrodynamics based on artificial compressibility method , 2017, Comput. Phys. Commun..

[29]  J. Monaghan.  Smoothed Particle Hydrodynamics and Its Diverse Applications , 2012 .

[30]  Xiangyu Hu,et al.  SPH modeling of fluid-structure interaction , 2018 .

[31]  Prabhu Ramachandran,et al.  Dual-Time Smoothed Particle Hydrodynamics for Incompressible Fluid Simulation , 2019, 1904.00861.

[32]  C. Antoci,et al.  Numerical simulation of fluid-structure interaction by SPH , 2007 .

[33]  Jose L. Cercos-Pita,et al.  AQUAgpusph, a new free 3D SPH solver accelerated with OpenCL , 2015, Comput. Phys. Commun..

[34]  Hitoshi Gotoh,et al.  Comparative study on accuracy and conservation properties of two particle regularization schemes and proposal of an optimized particle shifting scheme in ISPH context , 2017, J. Comput. Phys..

[35]  J. Monaghan.  SPH without a Tensile Instability , 2000 .

[36]  Nikolaus A. Adams,et al.  An incompressible multi-phase SPH method , 2007, J. Comput. Phys..

[37]  Piecewise Polynomial , 2014, Computer Vision, A Reference Guide.

[38]  Hu Dai,et al.  Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems , 2014, J. Comput. Phys..

[39]  Larry D. Libersky,et al.  Smooth particle hydrodynamics with strength of materials , 1991 .

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

[41]  S. Shao,et al.  Corrected Incompressible SPH method for accurate water-surface tracking in breaking waves , 2008 .

[42]  Arthur Veldman,et al.  A Volume-of-Fluid based simulation method for wave impact problems , 2005 .

[43]  L. Libersky,et al.  Smoothed Particle Hydrodynamics: Some recent improvements and applications , 1996 .

[44]  Abbas Khayyer,et al.  Enhancement of pressure calculation in projection-based particle methods by incorporation of background mesh scheme , 2019, Applied Ocean Research.

[45]  Nikolaus A. Adams,et al.  A generalized wall boundary condition for smoothed particle hydrodynamics , 2012, J. Comput. Phys..

[46]  Salvatore Marrone,et al.  The δplus-SPH model: Simple procedures for a further improvement of the SPH scheme , 2017 .

[47]  V. Springel.  Smoothed Particle Hydrodynamics in Astrophysics , 2010, 1109.2219.

[48]  Chi Zhang,et al.  A weakly compressible SPH method for violent multi-phase flows with high density ratio , 2019, J. Comput. Phys..

[49]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments , 2010 .

[50]  S. Cummins,et al.  An SPH Projection Method , 1999 .

[51]  R. Mittal,et al.  Benchmarking a Coupled Immersed-Boundary-Finite-Element Solver for Large-Scale Flow-Induced Deformation , 2012 .

[52]  Ivo F. Sbalzarini,et al.  PPM - A highly efficient parallel particle-mesh library for the simulation of continuum systems , 2006, J. Comput. Phys..

[53]  L. Verlet.  Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

[54]  Jean-Paul Vila,et al.  ON PARTICLE WEIGHTED METHODS AND SMOOTH PARTICLE HYDRODYNAMICS , 1999 .

[55]  A. Colagrossi,et al.  Numerical simulation of interfacial flows by smoothed particle hydrodynamics , 2003 .

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

[57]  Antonio Souto-Iglesias,et al.  Experimental investigation of dynamic pressure loads during dam break , 2013, 1308.0115.

[58]  Nikolaus A. Adams,et al.  A weakly compressible SPH method based on a low-dissipation Riemann solver , 2017, J. Comput. Phys..

[59]  R. Pajarola,et al.  Predictive-corrective incompressible SPH , 2009, SIGGRAPH 2009.

[60]  Nikolaus A. Adams,et al.  A generalized transport-velocity formulation for smoothed particle hydrodynamics , 2017, J. Comput. Phys..

[61]  William D. Mattson,et al.  Near-neighbor calculations using a modified cell-linked list method , 1999 .