Proper orthogonal decomposition of atomistic flow simulations

An adaptive proper orthogonal decomposition based on time windows (WPOD) for analysis of velocity fields from atomistic simulations is presented. The method effectively separates the field into ensemble average and fluctuation components, and can be applied to both stationary and non-stationary flows in simple and complex geometries. The criteria to distinguish POD modes representing ensemble average and fluctuation components are based on adaptive examination of eigenvalue decomposition, specifically on the rate of decay of POD eigenvalues and analysis of POD eigenvectors. The WPOD method is efficient and its superior accuracy leads to smooth field gradients that can be used effectively in multiscale formulations. The method has been applied in molecular dynamics and dissipative particle dynamics simulations. We demonstrate the method for several cases including steady and unsteady flow and red blood cell flow, but the same approach can be used in atomistic simulations of materials.

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

[2]  H. C. Andersen.  Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[3]  M. Parrinello,et al.  Enhanced sampling in the well-tempered ensemble. , 2009, Physical review letters.

[4]  P. Hünenberger.  Thermostat Algorithms for Molecular Dynamics Simulations , 2005 .

[5]  John B. Bell,et al.  Computational fluctuating fluid dynamics , 2010 .

[6]  L. Sirovich.  Turbulence and the dynamics of coherent structures. I. Coherent structures , 1987 .

[7]  G. Karniadakis,et al.  Analyzing Transient Turbulence in a Stenosed Carotid Artery by Proper Orthogonal Decomposition , 2009, Annals of Biomedical Engineering.

[8]  Michael E. Papka,et al.  A new computational paradigm in multiscale simulations: Application to brain blood flow , 2011, 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC).

[9]  George Em Karniadakis,et al.  A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. , 2010, Biophysical journal.

[10]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[11]  R Delgado-Buscalioni,et al.  Nonreflecting boundaries for ultrasound in fluctuating hydrodynamics of open systems. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  P. Español,et al.  Statistical Mechanics of Dissipative Particle Dynamics. , 1995 .

[13]  G. Karniadakis,et al.  Microflows and Nanoflows: Fundamentals and Simulation , 2001 .

[14]  L. Sirovich.  Turbulence and the dynamics of coherent structures. III. Dynamics and scaling , 1987 .

[15]  George Em Karniadakis,et al.  Direct construction of mesoscopic models from microscopic simulations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  K. Kremer,et al.  Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[18]  Daniele Venturi,et al.  On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate , 2006, Journal of Fluid Mechanics.

[19]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

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

[21]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .