MULTISCALE FLOW SIMULATIONS USING PARTICLES

▪ Abstract Flow simulations are one of the archetypal multiscale problems. Simulations of turbulent and unsteady separated flows have to resolve a multitude of interacting scales, whereas molecular phenomena determine the structure of shocks and the validity of the no-slip boundary condition. Particle simulations of continuum and molecular phenomena can be formulated by following the motion of interacting particles that carry the physical properties of the flow. In this article we review Lagrangian, multiresolution, particle methods such as vortex methods and smooth particle hydrodynamics for the simulation of continuous flows and molecular dynamics for the simulation of flows at the atomistic scale. We review hybrid molecular-continuum simulations with an emphasis on the computational aspects of the problem. We identify the common computational characteristics of particle methods and discuss their properties that enable the formulation of a systematic framework for multiscale flow simulations.

[1]  P. P. Ewald.  Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[2]  Louis Rosenhead,et al.  The Spread of Vorticity in the Wake Behind a Cylinder , 1930 .

[3]  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 .

[4]  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 .

[5]  B. Alder,et al.  Phase Transition for a Hard Sphere System , 1957 .

[6]  L. Verlet.  Computer "Experiments" on Classical Fluids. II. Equilibrium Correlation Functions , 1968 .

[7]  F. Stillinger,et al.  Molecular Dynamics Study of Liquid Water , 1971 .

[8]  A. Chorin.  Numerical study of slightly viscous flow , 1973, Journal of Fluid Mechanics.

[9]  R. W. Hockney,et al.  A 10000 particle molecular dynamics model with long range forces , 1973 .

[10]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[11]  J. Mccammon,et al.  Molecular dynamics with stochastic boundary conditions , 1982 .

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

[13]  Numerical solution for the problem of flame propagation by the random element method , 1984 .

[14]  M. Karplus,et al.  Stochastic boundary conditions for molecular dynamics simulations of ST2 water , 1984 .

[15]  A. Leonard.  Computing Three-Dimensional Incompressible Flows with Vortex Elements , 1985 .

[16]  J. Monaghan.  Particle methods for hydrodynamics , 1985 .

[17]  J. Monaghan,et al.  Extrapolating B splines for interpolation , 1985 .

[18]  P A Raviart.  Particle approximation of first order systems , 1986 .

[19]  R. Krasny.  A study of singularity formation in a vortex sheet by the point-vortex approximation , 1986, Journal of Fluid Mechanics.

[20]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[21]  J. T. Beale,et al.  A convergent 3-D vortex method with grid-free stretching , 1986 .

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

[23]  V. Rokhlin,et al.  Rapid Evaluation of Potential Fields in Three Dimensions , 1988 .

[24]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[25]  P. Degond,et al.  The weighted particle method for convection-diffusion equations , 1989 .

[26]  T. Sarpkaya.  Computational Methods With Vortices—The 1988 Freeman Scholar Lecture , 1989 .

[27]  P. Degond,et al.  The weighted particle method for convection-diffusion equations. II. The anisotropic case , 1989 .

[28]  Ryckaert,et al.  Evaluation of transport coefficients of simple fluids by molecular dynamics: Comparison of Green-Kubo and nonequilibrium approaches for shear viscosity. , 1989, Physical review. A, General physics.

[29]  Nathan Ida,et al.  A particle-grid superposition method for the Navier-Stokes equations , 1990 .

[30]  Thomas Y. Hou,et al.  Convergence of a variable blob vortex method for the Euler and Navier-Stokes equations , 1990 .

[31]  Christopher R. Anderson,et al.  An Implementation of the Fast Multipole Method without Multipoles , 1992, SIAM J. Sci. Comput..

[32]  Peter T. Cummings,et al.  Nonequilibrium molecular dynamics approaches to transport properties and non-Newtonian fluid rheology , 1992 .

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

[34]  Omar M. Knio,et al.  The three-dimensional structure of periodic vorticity layers under non-symmetric conditions , 1992, Journal of Fluid Mechanics.

[35]  Francesco Petruccione,et al.  A stochastic approach to computational fluid dynamics , 1992 .

[36]  P. Cummings,et al.  Nonequilibrium Molecular Dynamics Properties and Non-Newtonian Fluid Approaches to Transport Rheology , 1992 .

[37]  T. Darden,et al.  Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems , 1993 .

[38]  Abhinandan Jain,et al.  Protein simulations using techniques suitable for very large systems: The cell multipole method for nonbond interactions and the Newton‐Euler inverse mass operator method for internal coordinate dynamics , 1994, Proteins.

[39]  G. Bird.  Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[40]  P. Koumoutsakos,et al.  Boundary Conditions for Viscous Vortex Methods , 1994 .

[41]  Francesco Petruccione,et al.  How to build master equations for complex systems , 1995 .

[42]  O'Connell,et al.  Molecular dynamics-continuum hybrid computations: A tool for studying complex fluid flows. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[43]  Petros Koumoutsakos,et al.  Flow past an Impulsively Started Cylinder , 1995 .

[44]  J. Banavar,et al.  Corner flow in the sliding plate problem , 1995 .

[45]  Christopher R. Anderson,et al.  A High Order Explicit Method for the Computation of Flow About a Circular Cylinder , 1996 .

[46]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[47]  Georges-Henri Cottet,et al.  Artificial Viscosity Models for Vortex and Particle Methods , 1996 .

[48]  W. Cleveland,et al.  Smoothing by Local Regression: Principles and Methods , 1996 .

[49]  Paul Fischer,et al.  An Overlapping Schwarz Method for Spectral Element Solution of the Incompressible Navier-Stokes Equations , 1997 .

[50]  A. Patera,et al.  Heterogeneous Atomistic-Continuum Representations for Dense Fluid Systems , 1997 .

[51]  M. Klein,et al.  Modified nonequilibrium molecular dynamics for fluid flows with energy conservation , 1997 .

[52]  John Strain,et al.  Fast Adaptive 2D Vortex Methods , 1997 .

[53]  Patrick B. Warren,et al.  Dissipative particle dynamics , 1998 .

[54]  Sidney Yip,et al.  Coupling continuum to molecular-dynamics simulation: Reflecting particle method and the field estimator , 1998 .

[55]  N. Hadjiconstantinou.  Regular Article: Hybrid Atomistic–Continuum Formulations and the Moving Contact-Line Problem , 1999 .

[56]  Sidney Yip,et al.  Nearly exact solution for coupled continuum/MD fluid simulation , 1999 .

[57]  T. Darden,et al.  Molecular dynamics simulations of biomolecules: long-range electrostatic effects. , 1999, Annual review of biophysics and biomolecular structure.

[58]  Alejandro L. Garcia,et al.  Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo , 1999 .

[59]  Nicolas G. Hadjicostantinou.  COMBINING ATOMISTIC AND CONTINUUM SIMULATIONS OF CONTACT-LINE MOTION , 1999 .

[60]  Eirik Grude Flekkøy,et al.  Hybrid model for combined particle and continuum dynamics , 2000 .

[61]  Petros Koumoutsakos,et al.  Vortex Methods: Theory and Practice , 2000 .

[62]  Petros Koumoutsakos,et al.  Vortex Methods with Spatially Varying Cores , 2000 .

[63]  S. Maruyama.  MOLECULAR DYNAMICS METHOD FOR MICROSCALE HEAT TRANSFER , 2000 .

[64]  T. Colonius,et al.  A VORTEX PARTICLE METHOD FOR COMPRESSIBLE FLOWS , 2001 .

[65]  Georges-Henri Cottet,et al.  Blending Finite-Difference and Vortex Methods for Incompressible Flow Computations , 2000, SIAM J. Sci. Comput..

[66]  S. Osher,et al.  Level set methods: an overview and some recent results , 2001 .

[67]  Petros Koumoutsakos,et al.  Simulation of pollutant transport using a particle method , 2001 .

[68]  G. Hummer,et al.  Water conduction through the hydrophobic channel of a carbon nanotube , 2001, Nature.

[69]  Petros Koumoutsakos,et al.  Three-dimensional vortex methods for particle-laden flows with two-way coupling , 2001 .

[70]  P Español,et al.  Thermodynamically consistent mesoscopic fluid particle model. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  Thomas Y. Hou,et al.  An efficient dynamically adaptive mesh for potentially singular solutions , 2001 .

[72]  MOLECULAR DYNAMICS SIMULATIONS OF ATOMIZATION AND SPRAY PHENOMENA , 2001 .

[73]  Michael S. Warren,et al.  Vortex Methods for Direct Numerical Simulation of Three-Dimensional Bluff Body Flows , 2002 .

[74]  Ian M. Mitchell,et al.  A hybrid particle level set method for improved interface capturing , 2002 .

[75]  Nicholas Quirke,et al.  FLUID FLOW IN NANOPORES: ACCURATE BOUNDARY CONDITIONS FOR CARBON NANOTUBES , 2002 .

[76]  Tim Colonius,et al.  A general deterministic treatment of derivatives in particle methods , 2002 .

[77]  Andrei Khodakovsky,et al.  Hybrid meshes: multiresolution using regular and irregular refinement , 2002, SCG '02.

[78]  Georges-Henri Cottet,et al.  A particle model for fluid-structure interaction , 2002 .

[79]  Thomas Y. Hou,et al.  Multiscale Modeling and Computation of Incompressible Flow , 2002 .

[80]  S. Hess,et al.  Viscoelastic flows studied by smoothed particle dynamics , 2002 .

[81]  T. Schlick.  Molecular modeling and simulation , 2002 .

[82]  Geri Wagner,et al.  Coupling molecular dynamics and continuum dynamics , 2002 .

[83]  Petros Koumoutsakos,et al.  Remeshed smoothed particle hydrodynamics for the simulation of viscous and heat conducting flows , 2002 .

[84]  K. Kremer,et al.  Multiscale simulation in polymer science , 2002 .

[85]  S. Glotzer,et al.  Molecular and Mesoscale Simulation Methods for Polymer Materials , 2002 .

[86]  Georges-Henri Cottet,et al.  A comparison of spectral and vortex methods in three-dimensional incompressible flows , 2002 .

[87]  Pep Español,et al.  Smoothed dissipative particle dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[88]  I. Babuska,et al.  Meshless and Generalized Finite Element Methods: A Survey of Some Major Results , 2003 .

[89]  Alejandro L. Garcia,et al.  Statistical error in particle simulations of hydrodynamic phenomena , 2002, cond-mat/0207430.

[90]  E Weinan,et al.  The Heterognous Multiscale Methods , 2003 .

[91]  P. Coveney,et al.  Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[92]  Georges-Henri Cottet,et al.  Advances in direct numerical simulations of 3D wall-bounded flows by Vortex-in-Cell methods , 2004 .

[93]  Petros Koumoutsakos,et al.  Hydrophobic hydration of C60 and carbon nanotubes in water , 2004 .

[94]  P. Koumoutsakos,et al.  Hydrodynamic properties of carbon nanotubes. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[95]  Graham V. Candler,et al.  A hybrid continuum/particle approach for modeling subsonic, rarefied gas flows , 2004 .

[96]  Petros Koumoutsakos,et al.  Nanoscale Fluid Mechanics , 2004 .

[97]  Gianluca Iaccarino,et al.  IMMERSED BOUNDARY METHODS , 2005 .

[98]  P. Koumoutsakos,et al.  Hybrid atomistic-continuum method for the simulation of dense fluid flows , 2005 .

[99]  Michael Bergdorf,et al.  Multilevel Adaptive Particle Methods for Convection-Diffusion Equations , 2005, Multiscale Model. Simul..

[100]  J. Tinsley Oden,et al.  An hp Adaptive Method Using Clouds C , 2006 .