Communications on Applied Mathematics and Computation ›› 2024, Vol. 6 ›› Issue (3): 1521-1550.doi: 10.1007/s42967-023-00251-3

• ORIGINAL PAPERS • Previous Articles     Next Articles

Optimization of Artificial Viscosity in Production Codes Based on Gaussian Regression Surrogate Models

Vitaliy Gyrya1, Evan Lieberman2, Mark Kenamond3, Mikhail Shashkov2   

  1. 1 Applied Mathematics and Plasma Physics, Theoretical Division, Mail Stop B284, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;
    2 Continuum Models and Numerical Methods Group, X-Computational Physics Division, Mail Stop F644, Los Alamos National Laboratory, Los Alamos, NM 87545, USA;
    3 Lagrangian Codes Group, X-Computational Physics Division, Mail Stop T086, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
  • Received:2022-09-06 Revised:2023-01-05 Accepted:2023-01-06 Published:2024-12-20
  • Contact: Mikhail Shashkov,shashkov@lanl.gov E-mail:shashkov@lanl.gov
  • Supported by:
    This work was performed under the auspices of the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under Contract No. 89233218CNA000001. The Authors gratefully acknowledge the support of the US Department of Energy National Nuclear Security Administration Advanced Simulation and Computing Program. LA-UR-22-33159.

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Abstract: To accurately model flows with shock waves using staggered-grid Lagrangian hydrodynamics, the artificial viscosity has to be introduced to convert kinetic energy into internal energy, thereby increasing the entropy across shocks. Determining the appropriate strength of the artificial viscosity is an art and strongly depends on the particular problem and experience of the researcher. The objective of this study is to pose the problem of finding the appropriate strength of the artificial viscosity as an optimization problem and solve this problem using machine learning (ML) tools, specifically using surrogate models based on Gaussian Process regression (GPR) and Bayesian analysis. We describe the optimization method and discuss various practical details of its implementation. The shock-containing problems for which we apply this method all have been implemented in the LANL code FLAG (Burton in Connectivity structures and differencing techniques for staggered-grid free-Lagrange hydrodynamics, Tech. Rep. UCRL-JC-110555, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1992, in Consistent finite-volume discretization of hydrodynamic conservation laws for unstructured grids, Tech. Rep. CRLJC-118788, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, Multidimensional discretization of conservation laws for unstructured polyhedral grids, Tech. Rep. UCRL-JC-118306, Lawrence Livermore National Laboratory, Livermore, CA, 1992, 1994, in FLAG, a multi-dimensional, multiple mesh, adaptive free-Lagrange, hydrodynamics code. In: NECDC, 1992). First, we apply ML to find optimal values to isolated shock problems of different strengths. Second, we apply ML to optimize the viscosity for a one-dimensional (1D) propagating detonation problem based on Zel’dovich-von NeumannDoring (ZND) (Fickett and Davis in Detonation: theory and experiment. Dover books on physics. Dover Publications, Mineola, 2000) detonation theory using a reactive burn model. We compare results for default (currently used values in FLAG) and optimized values of the artificial viscosity for these problems demonstrating the potential for significant improvement in the accuracy of computations.

Key words: Optimization, Artificial viscosity, Gaussian regression surrigate model

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