LOQUAT: an open-source GPU-accelerated SPH solver for geotechnical modeling

Smoothed particle hydrodynamics (SPH) is a meshless method gaining popularity recently in geotechnical modeling. It is suitable to solve problems involving large deformation, free-surface, cracking and fragmentation. To promote the research and application of SPH in geotechnical engineering, we present LOQUAT, an open-source three-dimensional GPU accelerated SPH solver. LOQUAT employs the standard SPH formulations for solids with two geomechnical constitutive models which are the Drucker–Prager model and a hypoplastic model. Three stabilization techniques, namely, artificial viscosity, artificial pressure and stress regularization are included. A generalized boundary particle method is presented to model static and moving boundaries with arbitrary geometry. LOQUAT employs GPU acceleration technique to greatly increase the computational efficiency. Numerical examples show that the solver is convergent, stable and highly efficient. With a mainstream GPU, it can simulate large scale problems with tens of millions of particles, and easily performs more than one thousand times faster than serial CPU code.

[1]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae , 1946 .

[2]  I. J. Schoenberg.  Contributions to the problem of approximation of equidistant data by analytic functions. Part B. On the problem of osculatory interpolation. A second class of analytic approximation formulae , 1946 .

[3]  D. C. Drucker,et al.  Soil mechanics and plastic analysis or limit design , 1952 .

[4]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

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

[6]  L. Hernquist,et al.  TREESPH: A Unification of SPH with the Hierarchical Tree Method , 1989 .

[7]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[8]  L. Libersky,et al.  High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response , 1993 .

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

[10]  Wei Wu,et al.  A simple hypoplastic constitutive model for sand , 1994 .

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

[12]  Wei Wu,et al.  Hypoplastic constitutive model with critical state for granular materials , 1996 .

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

[14]  Larry D. Libersky,et al.  Recent improvements in SPH modeling of hypervelocity impact , 1997 .

[15]  B. Schrefler,et al.  The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media , 1998 .

[16]  Tadahiko Shiomi,et al.  Practical Programming in Computational Geomechanics: With Special Reference to Earthquake Engineering , 1999 .

[17]  D. Potts,et al.  Finite Element Analysis in Geotechnical Engineering: Volume Two - Application , 1999 .

[18]  Joseph P. Morris,et al.  Parallel simulations of pore-scale flow through porous media , 1999 .

[19]  J. Monaghan.  Smoothed particle hydrodynamics , 2005 .

[20]  J. Brackbill,et al.  The material-point method for granular materials , 2000 .

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

[22]  J. Monaghan,et al.  SPH elastic dynamics , 2001 .

[23]  V. Springel,et al.  GADGET: a code for collisionless and gasdynamical cosmological simulations , 2000, astro-ph/0003162.

[24]  Guirong Liu,et al.  Smoothed Particle Hydrodynamics: A Meshfree Particle Method , 2003 .

[25]  E. Oñate,et al.  The particle finite element method. An overview , 2004 .

[26]  S. Bardenhagen,et al.  The Generalized Interpolation Material Point Method , 2004 .

[27]  H. Huppert,et al.  Axisymmetric collapses of granular columns , 2004, Journal of Fluid Mechanics.

[28]  Z. Więckowski.  The material point method in large strain engineering problems , 2004 .

[29]  T. Quinn,et al.  Gasoline: a flexible, parallel implementation of TreeSPH , 2003, astro-ph/0303521.

[30]  O. Hungr,et al.  A model for the analysis of rapid landslide motion across three-dimensional terrain , 2004 .

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

[32]  T. Matsushima,et al.  A 2D Smoothed Particle Hydrodynamics method for liquefaction induced lateral spreading analysis , 2005 .

[33]  Hirotaka Sakai,et al.  DEVELOPMENT OF SEEPAGE FAILURE ANALYSIS METHOD OF GROUND WITH SMOOTHED PARTICLE HYDRODYNAMICS , 2006 .

[34]  Ha H. Bui,et al.  Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model , 2008 .

[35]  D. Owen,et al.  Computational methods for plasticity : theory and applications , 2008 .

[36]  M. Pastor,et al.  A depth‐integrated, coupled SPH model for flow‐like landslides and related phenomena , 2009 .

[37]  B. Rogers,et al.  State-of-the-art of classical SPH for free-surface flows , 2010 .

[38]  Martin Robinson,et al.  Turbulence and viscous mixing using smoothed particle hydrodynamics , 2010 .

[39]  Simon Green,et al.  Particle Simulation using CUDA , 2010 .

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

[41]  Paul W. Cleary,et al.  Effect of rock shapes on brittle fracture using Smoothed Particle Hydrodynamics , 2010 .

[42]  M. Naaim,et al.  Numerical simulations of granular free-surface flows using smoothed particle hydrodynamics , 2011 .

[43]  Eugenio Rustico,et al.  Numerical simulation of lava flow using a GPU SPH model , 2011 .

[44]  J. Wells,et al.  Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH) , 2011 .

[45]  Wei Wu,et al.  An Updated Hypoplastic Constitutive Model, Its Implementation and Application , 2011 .

[46]  E. Oñate,et al.  Possibilities of the particle finite element method for fluid–soil–structure interaction problems , 2011 .

[47]  Qiang Xu,et al.  Run-out analysis of flow-like landslides triggered by the Ms 8.0 2008 Wenchuan earthquake using smoothed particle hydrodynamics , 2012, Landslides.

[48]  Yu Huang,et al.  Flow analysis of liquefied soils based on smoothed particle hydrodynamics , 2011 .

[49]  J. Andrade,et al.  On the rheology of dilative granular media: Bridging solid- and fluid-like behavior , 2012 .

[50]  W. Dehnen,et al.  Improving convergence in smoothed particle hydrodynamics simulations without pairing instability , 2012, 1204.2471.

[51]  Robert A. Dalrymple,et al.  SPHysics - development of a free-surface fluid solver - Part 2: Efficiency and test cases , 2012, Comput. Geosci..

[52]  Benedict D. Rogers,et al.  SPHysics - development of a free-surface fluid solver - Part 1: Theory and formulations , 2012, Comput. Geosci..

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

[54]  Wei Chen,et al.  Numerical Simulations for Large Deformation of Granular Materials Using Smoothed Particle Hydrodynamics Method , 2012 .

[55]  M. Pastor,et al.  A stabilized Fractional Step, Runge–Kutta Taylor SPH algorithm for coupled problems in geomechanics , 2012 .

[56]  Moncho Gómez-Gesteira,et al.  New multi-GPU implementation for smoothed particle hydrodynamics on heterogeneous clusters , 2013, Comput. Phys. Commun..

[57]  Ha H. Bui,et al.  An improved SPH method for saturated soils and its application to investigate the mechanisms of embankment failure: Case of hydrostatic pore‐water pressure , 2013 .

[58]  Ha H. Bui,et al.  A novel computational approach for large deformation and post‐failure analyses of segmental retaining wall systems , 2014 .

[59]  Jian Wang,et al.  Frictional contact algorithms in SPH for the simulation of soil–structure interaction , 2014 .

[60]  L. Hernquist,et al.  NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS , 2014, 1410.4222.

[61]  L. Cascini,et al.  SPH run-out modelling of channelised landslides of the flow type , 2014 .

[62]  C. Bojanowski.  Numerical modeling of large deformations in soil structure interaction problems using FE, EFG, SPH, and MM-ALE formulations , 2014 .

[63]  N. Prime,et al.  Unified Model for Geomaterial Solid/Fluid States and the Transition in Between , 2014 .

[64]  Xiaoping Zhou,et al.  Numerical Simulation of Crack Growth and Coalescence in Rock-Like Materials Containing Multiple Pre-existing Flaws , 2015, Rock Mechanics and Rock Engineering.

[65]  Utkarsh Ayachit,et al.  The ParaView Guide: A Parallel Visualization Application , 2015 .

[66]  L. Minatti,et al.  A SPH model for the simulation of free surface granular flows in a dense regime , 2015 .

[67]  Wei Wu,et al.  A SPH approach for large deformation analysis with hypoplastic constitutive model , 2015 .

[68]  P. Hopkins.  A new class of accurate, mesh-free hydrodynamic simulation methods , 2014, 1409.7395.

[69]  Stephen M. Longshaw,et al.  DualSPHysics: Open-source parallel CFD solver based on Smoothed Particle Hydrodynamics (SPH) , 2015, Comput. Phys. Commun..

[70]  Chong Peng,et al.  Numerical simulation of free surface seepage in saturated soil using Smoothed Particle Hydrodynamics , 2015 .

[71]  Chong Peng,et al.  Smoothed Particle Hydrodynamics Simulation of Water-Soil Mixture Flows , 2016 .

[72]  Weijie Zhang,et al.  Numerical analysis on seepage failures of dike due to water level-up and rainfall using a water–soil-coupled smoothed particle hydrodynamics model , 2016 .

[73]  K. Szewc.  Smoothed particle hydrodynamics modeling of granular column collapse , 2016, Granular Matter.

[74]  Chong Peng,et al.  Unified modelling of granular media with Smoothed Particle Hydrodynamics , 2016 .

[75]  Cuong T. Nguyen,et al.  A new SPH-based approach to simulation of granular flows using viscous damping and stress regularisation , 2017, Landslides.

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

[77]  D. Violeau,et al.  Smoothed particle hydrodynamics (SPH) for free-surface flows: past, present and future , 2016 .

[78]  Chong Peng,et al.  Dilatancy and compaction effects on the submerged granular column collapse , 2017 .

[79]  Chong Peng,et al.  Large Deformation Modeling of Soil-Machine Interaction in Clay , 2017 .

[80]  Wei Wu,et al.  A basic hypoplastic constitutive model for sand , 2017 .

[81]  M. Gholami Korzani,et al.  SPH approach for simulating hydro-mechanical processes with large deformations and variable permeabilities , 2017 .

[82]  Chong Peng,et al.  Multiphase SPH modeling of free surface flow in porous media with variable porosity , 2017 .

[83]  Xiaoping Zhou,et al.  Numerical Simulation of Failure Process of Rock-Like Materials Subjected to Impact Loads , 2017 .

[84]  Xiaoping Zhou,et al.  Analysis of the numerical stability of soil slope using virtual-bond general particle dynamics , 2018, Engineering Geology.

[85]  S. Lourenço,et al.  Soil wettability in ground engineering: fundamentals, methods, and applications , 2018 .

[86]  Fue-Sang Lien,et al.  Simulations for soil explosion and its effects on structures using SPH method , 2018 .

[87]  Alomir H. Fávero Neto,et al.  Continuum hydrodynamics of dry granular flows employing multiplicative elastoplasticity , 2018, Acta Geotechnica.

[88]  Bingyin Zhang,et al.  A stabilized TL–WC SPH approach with GPU acceleration for three-dimensional fluid–structure interaction , 2019, Journal of Fluids and Structures.