Simulation-driven optimization of high-order meshes in ALE hydrodynamics

Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio; Mittal, Ketan; Rieben, Robert; Tomov, Vladimir

doi:10.1016/j.compfluid.2020.104602

Simulation-driven optimization of high-order meshes in ALE hydrodynamics

Journal Article · Thu Jun 11 00:00:00 EDT 2020 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2020.104602· OSTI ID:1773258

Dobrev, Veselin ^[1]; Knupp, Patrick ^[2]; Kolev, Tzanio ^[1]; Mittal, Ketan ^[1]; Rieben, Robert ^[1]; Tomov, Vladimir ^[1]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Dihedral LLC, Bozeman, MT (United States)

Here we propose tools for high-order mesh optimization and demonstrate their benefits in the context of multi-material Arbitrary Lagrangian-Eulerian (ALE) compressible shock hydrodynamic applications. The mesh optimization process is driven by information provided by the simulation which uses the optimized mesh, such as shock positions, material regions, known error estimates, etc. These simulation features are usually represented discretely, for instance, as finite element functions on the Lagrangian mesh. The discrete nature of the input is critical for the practical applicability of the algorithms we propose and distinguishes this work from approaches that strictly require analytical information. Our methods are based on node movement through a high-order extension of the Target-Matrix Optimization Paradigm (TMOP). The proposed formulation is fully algebraic and relies only on local Jacobian matrices, so it is applicable to all types of mesh elements, in 2D and 3D, and any order of the mesh. We discuss the notions of constructing adaptive target matrices and obtaining their derivatives, reconstructing discrete data in intermediate meshes, node limiting that enables improvement of global mesh quality while preserving space-dependent local mesh features, and appropriate normalization of the objective function. The adaptivity methods are combined with automatic ALE triggers that can provide robustness of the mesh evolution and avoid excessive remap procedures. The benefits of the new high-order TMOP technology are illustrated on several simulations performed in the high-order ALE application BLAST.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1773258

Alternate ID(s):: OSTI ID: 1776278

Report Number(s):: LLNL-JRNL--800087; 1003307

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 208; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (32)

A Lagrangian Discontinuous Galerkin-type method on unstructured meshes to solve hydrodynamics problems Loubère, R.; Ovadia, J.; Abgrall, R. International Journal for Numerical Methods in Fluids, Vol. 44, Issue 6 https://doi.org/10.1002/fld.665	journal	February 2004
Stabilized shock hydrodynamics: I. A Lagrangian method Scovazzi, G.; Christon, M. A.; Hughes, T. J. R. Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 4-6 https://doi.org/10.1016/j.cma.2006.08.008	journal	January 2007
Entropy–viscosity method for the single material Euler equations in Lagrangian frame Guermond, Jean-Luc; Popov, Bojan; Tomov, Vladimir Computer Methods in Applied Mechanics and Engineering, Vol. 300 https://doi.org/10.1016/j.cma.2015.11.009	journal	March 2016
ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method Loubère, Raphaël; Maire, Pierre-Henri; Shashkov, Mikhail Journal of Computational Physics, Vol. 229, Issue 12 https://doi.org/10.1016/j.jcp.2010.03.011	journal	June 2010
A Method for the Numerical Calculation of Hydrodynamic Shocks VonNeumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, Issue 3 https://doi.org/10.1063/1.1699639	journal	March 1950
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N. SIAM Journal on Scientific Computing, Vol. 34, Issue 5 https://doi.org/10.1137/120864672	journal	January 2012
A cell-centred arbitrary Lagrangian–Eulerian (ALE) method Maire, Pierre-Henri; Breil, Jérôme; Galera, Stéphane International Journal for Numerical Methods in Fluids, Vol. 56, Issue 8 https://doi.org/10.1002/fld.1557	journal	January 2008
Multi-material closure model for high-order finite element Lagrangian hydrodynamics: CLOSURE MODEL FOR HIGH-ORDER FINITE ELEMENT HYDRODYNAMICS Dobrev, V. A.; Kolev, T. V.; Rieben, R. N. International Journal for Numerical Methods in Fluids, Vol. 82, Issue 10 https://doi.org/10.1002/fld.4236	journal	April 2016
Improved ALE mesh velocities for complex flows: Improved ALE mesh velocities for complex flows Bakosi, Jozsef; Waltz, Jacob; Morgan, Nathaniel International Journal for Numerical Methods in Fluids, Vol. 85, Issue 11 https://doi.org/10.1002/fld.4403	journal	June 2017
rp ‐adaptation for compressible flows Marcon, Julian; Castiglioni, Giacomo; Moxey, David International Journal for Numerical Methods in Engineering, Vol. 121, Issue 23 https://doi.org/10.1002/nme.6529	journal	September 2020
A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids Howell, B. P.; Ball, G. J. Journal of Computational Physics, Vol. 175, Issue 1 https://doi.org/10.1006/jcph.2001.6931	journal	January 2002
Introducing the target-matrix paradigm for mesh optimization via node-movement Knupp, Patrick Engineering with Computers, Vol. 28, Issue 4 https://doi.org/10.1007/s00366-011-0230-1	journal	September 2011
Mesh Smoothing for the Spectral Element Method Mittal, Ketan; Fischer, Paul Journal of Scientific Computing, Vol. 78, Issue 2 https://doi.org/10.1007/s10915-018-0812-9	journal	August 2018
An arbitrary Lagrangian-Eulerian computing method for all flow speeds Hirt, C. W.; Amsden, A. A.; Cook, J. L. Journal of Computational Physics, Vol. 14, Issue 3 https://doi.org/10.1016/0021-9991(74)90051-5	journal	March 1974
Computational methods in Lagrangian and Eulerian hydrocodes Benson, David J. Computer Methods in Applied Mechanics and Engineering, Vol. 99, Issue 2-3 https://doi.org/10.1016/0045-7825(92)90042-I	journal	September 1992
Variational method for untangling and optimization of spatial meshes Garanzha, V. A.; Kudryavtseva, L. N.; Utyuzhnikov, S. V. Journal of Computational and Applied Mathematics, Vol. 269 https://doi.org/10.1016/j.cam.2014.03.006	journal	October 2014
Discretizations for weighted condition number smoothing on general unstructured meshes Váchal, P.; Maire, P. -H. Computers & Fluids, Vol. 46, Issue 1 https://doi.org/10.1016/j.compfluid.2010.10.025	journal	July 2011
High-order curvilinear finite elements for axisymmetric Lagrangian hydrodynamics Dobrev, Veselin A.; Ellis, Truman E.; Kolev, Tzanio V. Computers & Fluids, Vol. 83 https://doi.org/10.1016/j.compfluid.2012.06.004	journal	August 2013
High order accurate direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes on moving curvilinear unstructured meshes Boscheri, Walter; Dumbser, Michael Computers & Fluids, Vol. 136 https://doi.org/10.1016/j.compfluid.2016.05.020	journal	September 2016
Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes Gaburro, Elena; Dumbser, Michael; Castro, Manuel J. Computers & Fluids, Vol. 159 https://doi.org/10.1016/j.compfluid.2017.09.022	journal	December 2017
Nonconforming Schwarz-spectral element methods for incompressible flow Mittal, Ketan; Dutta, Som; Fischer, Paul Computers & Fluids, Vol. 191 https://doi.org/10.1016/j.compfluid.2019.104237	journal	September 2019
A high-order cell-centered Lagrangian scheme for two-dimensional compressible fluid flows on unstructured meshes Maire, Pierre-Henri Journal of Computational Physics, Vol. 228, Issue 7 https://doi.org/10.1016/j.jcp.2008.12.007	journal	April 2009
A comparative study of interface reconstruction methods for multi-material ALE simulations Kucharik, Milan; Garimella, Rao V.; Schofield, Samuel P. Journal of Computational Physics, Vol. 229, Issue 7 https://doi.org/10.1016/j.jcp.2009.07.009	journal	April 2010
A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction Galera, Stéphane; Maire, Pierre-Henri; Breil, Jérôme Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.04.019	journal	August 2010
High order curvilinear finite elements for elastic–plastic Lagrangian dynamics Dobrev, Veselin A.; Kolev, Tzanio V.; Rieben, Robert N. Journal of Computational Physics, Vol. 257 https://doi.org/10.1016/j.jcp.2013.01.015	journal	January 2014
Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics Barlow, Andrew; Hill, Ryan; Shashkov, Mikhail Journal of Computational Physics, Vol. 276 https://doi.org/10.1016/j.jcp.2014.07.031	journal	November 2014
A variational multiscale finite element method for monolithic ALE computations of shock hydrodynamics using nodal elements Zeng, X.; Scovazzi, G. Journal of Computational Physics, Vol. 315 https://doi.org/10.1016/j.jcp.2016.03.052	journal	June 2016
Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows Barlow, Andrew J.; Maire, Pierre-Henri; Rider, William J. Journal of Computational Physics, Vol. 322 https://doi.org/10.1016/j.jcp.2016.07.001	journal	October 2016
Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert Journal of Computational Physics, Vol. 335 https://doi.org/10.1016/j.jcp.2017.01.049	journal	April 2017
Polyconvex potentials, invertible deformations, and thermodynamically consistent formulation of the nonlinear elasticity equations Garanzha, V. A. Computational Mathematics and Mathematical Physics, Vol. 50, Issue 9 https://doi.org/10.1134/S0965542510090095	journal	September 2010
High-Order Multi-Material ALE Hydrodynamics Anderson, Robert W.; Dobrev, Veselin A.; Kolev, Tzanio V. SIAM Journal on Scientific Computing, Vol. 40, Issue 1 https://doi.org/10.1137/17M1116453	journal	January 2018
The Target-Matrix Optimization Paradigm for High-Order Meshes Dobrev, Veselin; Knupp, Patrick; Kolev, Tzanio SIAM Journal on Scientific Computing, Vol. 41, Issue 1 https://doi.org/10.1137/18M1167206	journal	January 2019

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