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Lagrangian large eddy simulations via physics-informed machine learning

Journal Article · · Proceedings of the National Academy of Sciences of the United States of America
 [1];  [2];  [3];  [4];  [2];  [4];  [3]
  1. Information Sciences Group, Computer, Computational and Statistical Sciences Division (CCS-3), Los Alamos National Laboratory, Los Alamos, NM 87545
  2. Graduate Interdisciplinary Program in Applied Mathematics and Department of Mathematics, University of Arizona, Tucson, AZ 85721, Computational Physics and Methods Group, Computer, Computational and Statistical Sciences Division (CCS-2), Los Alamos National Laboratory, Los Alamos, NM 87545
  3. Graduate Interdisciplinary Program in Applied Mathematics and Department of Mathematics, University of Arizona, Tucson, AZ 85721
  4. Computational Physics and Methods Group, Computer, Computational and Statistical Sciences Division (CCS-2), Los Alamos National Laboratory, Los Alamos, NM 87545

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
89233218CNA000001
OSTI ID:
2001327
Alternate ID(s):
OSTI ID: 2439468
Report Number(s):
LA-UR--23-25907; e2213638120
Journal Information:
Proceedings of the National Academy of Sciences of the United States of America, Journal Name: Proceedings of the National Academy of Sciences of the United States of America Journal Issue: 34 Vol. 120; ISSN 0027-8424
Publisher:
Proceedings of the National Academy of SciencesCopyright Statement
Country of Publication:
United States
Language:
English

References (66)

Numerical modelling of complex turbulent free-surface flows with the SPH method: an overview journal January 2006
Catastrophic Disruptions Revisited journal November 1999
SPH numerical investigation of the velocity field and vorticity generation within a hydrofoil-induced spilling breaker journal November 2015
Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments journal February 2010
Compact finite difference schemes with spectral-like resolution journal November 1992
An examination of forcing in direct numerical simulations of turbulence journal January 1988
A deterministic forcing scheme for direct numerical simulations of turbulence journal January 1998
Simulation of near-shore solitary wave mechanics by an incompressible SPH method journal October 2002
Restoring particle consistency in smoothed particle hydrodynamics journal January 2006
Numerical modeling of water waves with the SPH method journal February 2006
DNS and LES of 3-D wall-bounded turbulence using Smoothed Particle Hydrodynamics journal July 2015
Smoothed particle hydrodynamics method for fluid flows, towards industrial applications: Motivations, current state, and challenges journal September 2016
Smoothed particle hydrodynamics and magnetohydrodynamics journal February 2012
Unified semi-analytical wall boundary conditions applied to 2-D incompressible SPH journal March 2014
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations journal February 2019
Rayleigh–Taylor instability with gravity reversal journal March 2021
Turbulence: The Legacy of A. N. Kolmogorov book January 1996
Turbulence structure behind the shock in canonical shock–vortical turbulence interaction journal September 2014
Reynolds averaged turbulence modelling using deep neural networks with embedded invariance journal October 2016
Super-resolution reconstruction of turbulent flows with machine learning journal May 2019
Density effects on post-shock turbulence structure and dynamics journal October 2019
Effects of Atwood and Reynolds numbers on the evolution of buoyancy-driven homogeneous variable-density turbulence journal May 2020
Variable-density effects in incompressible non-buoyant shear-driven turbulent mixing layers journal August 2020
Interpreting neural network models of residual scalar flux journal November 2020
Phantom : A Smoothed Particle Hydrodynamics and Magnetohydrodynamics Code for Astrophysics journal January 2018
The sonic scale of interstellar turbulence journal January 2021
Physics-informed machine learning journal May 2021
SPH compressible turbulence journal September 2002
Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties journal September 2005
Scaling laws and intermittency in highly compressible turbulence conference January 2007
Forcing for statistically stationary compressible isotropic turbulence journal November 2010
Smoothed particle hydrodynamics method from a large eddy simulation perspective journal March 2017
Smoothed particle hydrodynamics (SPH) for complex fluid flows: Recent developments in methodology and applications journal January 2019
Lagrangian tetrad dynamics and the phenomenology of turbulence journal August 1999
Smoothed particle hydrodynamics method from a large eddy simulation perspective. Generalization to a quasi-Lagrangian model journal January 2021
Spatio-temporal deep learning models of 3D turbulence with physics informed diagnostics journal October 2020
Inside the supernova: A powerful convective engine journal November 1994
The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions journal November 1999
Forming the First Stars in the Universe: The Fragmentation of Primordial Gas journal December 1999
Adaptive Smoothed Particle Hydrodynamics: Methodology. II.
  • Owen, J. Michael; Villumsen, Jens V.; Shapiro, Paul R.
  • The Astrophysical Journal Supplement Series, Vol. 116, Issue 2 https://doi.org/10.1086/313100
journal June 1998
Smoothed particle hydrodynamics: theory and application to non-spherical stars journal December 1977
Modelling accretion in protobinary systems journal November 1995
Mixing matters journal July 2021
On the universality of supersonic turbulence journal September 2013
A new class of accurate, mesh-free hydrodynamic simulation methods journal April 2015
A comparison between grid and particle methods on the small-scale dynamo in magnetized supersonic turbulence journal June 2016
Review of smoothed particle hydrodynamics: towards converged Lagrangian flow modelling
  • Lind, Steven J.; Rogers, Benedict D.; Stansby, Peter K.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2241 https://doi.org/10.1098/rspa.2019.0801
journal September 2020
Spectra and statistics in compressible isotropic turbulence journal January 2017
Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data journal March 2017
Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor journal September 2021
Embedding hard physical constraints in neural network coarse-graining of three-dimensional turbulence journal January 2023
Physics-informed machine learning with smoothed particle hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence journal May 2023
Universal scaling laws in fully developed turbulence journal January 1994
Artificial neural networks for solving ordinary and partial differential equations journal January 1998
Machine Learning Paradigms for Speech Recognition: An Overview journal May 2013
The cosmological simulation code gadget-2 journal December 2005
Star formation and feedback in smoothed particle hydrodynamic simulations – I. Isolated galaxies journal November 2006
Resolving high Reynolds numbers in smoothed particle hydrodynamics simulations of subsonic turbulence journal December 2011
The Equations of Motion of Particles in Smoothed Particle Hydrodynamics journal September 1991
Smoothed Particle Hydrodynamics: A Meshfree Particle Method book October 2003
Data-driven fluid simulations using regression forests journal November 2015
Turbulence Modeling in the Age of Data journal January 2019
Turbulence with Large Thermal and Compositional Density Variations journal January 2020
Smoothed Particle Hydrodynamics and Its Diverse Applications journal January 2012
Smoothed Particle Hydrodynamics journal September 1992
L AGRANGIAN I NVESTIGATIONS OF T URBULENCE journal January 2002