A modern concept of Lagrangian hydrodynamics

Margolin, Len G.; Canfield, Jesse M.

doi:10.1111/sapm.12754

A modern concept of Lagrangian hydrodynamics

Journal Article · Thu Aug 29 00:00:00 EDT 2024 · Studies in Applied Mathematics

DOI:https://doi.org/10.1111/sapm.12754· OSTI ID:2530365

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Here, we offer a modern interpretation of Lagrangian hydrodynamics as employed in Lagrangian simulations of compressible fluid flow. Our main result is to show that artificial viscosity, traditionally viewed as a numerical artifice to control unphysical oscillations in flows with shocks, actually represents a physical process and is necessary to derive accurate simulations in any compressible flow. We begin by reviewing the origins of two numerical devices, artificial viscosity and finite-volume methods. We proceed to construct a mathematical (PDE) model that incorporates those numerics and in which a new length scale, the observer, arises representing the discretization. Associated with that length scale, there are new inviscid fluxes that are the artificial viscosity as first formulated by Richtmyer and an artificial heat flux postulated by Noh but typically not included in Lagrangian codes. We discuss the connection of our results to bivelocity hydrodynamics. We conclude with some speculation as to the direction of future developments in multidimensional Lagrangian codes as computers get faster and have larger memories.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

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

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2530365

Alternate ID(s):: OSTI ID: 2438618

Report Number(s):: LA-UR--24-25608

Journal Information:: Studies in Applied Mathematics, Journal Name: Studies in Applied Mathematics Journal Issue: 4 Vol. 153; ISSN 0022-2526

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

References (34)

Weak solutions of nonlinear hyperbolic equations and their numerical computation Lax, Peter D. Communications on Pure and Applied Mathematics, Vol. 7, Issue 1 https://doi.org/10.1002/cpa.3160070112	journal	February 1954
Systems of conservation laws Lax, Peter; Wendroff, Burton Communications on Pure and Applied Mathematics, Vol. 13, Issue 2 https://doi.org/10.1002/cpa.3160130205	journal	May 1960
A rationale for implicit turbulence modelling Margolin, Len G.; Rider, William J. International Journal for Numerical Methods in Fluids, Vol. 39, Issue 9 https://doi.org/10.1002/fld.331	journal	January 2002
Formulations of Artificial Viscosity for Multi-dimensional Shock Wave Computations Caramana, E. J.; Shashkov, M. J.; Whalen, P. P. Journal of Computational Physics, Vol. 144, Issue 1 https://doi.org/10.1006/jcph.1998.5989	journal	July 1998
Degenerate Parabolic Equations DiBenedetto, Emmanuele Universitext https://doi.org/10.1007/978-1-4612-0895-2	book	January 1993
Sto�welle und Detonation Becker, R. Zeitschrift f�r Physik, Vol. 8, Issue 1 https://doi.org/10.1007/BF01329605	journal	December 1922
Artificial viscosity—then and now Margolin, L. G.; Lloyd-Ronning, N. M. Meccanica, Vol. 58, Issue 6 https://doi.org/10.1007/s11012-022-01541-5	journal	June 2022
PIC and its progeny Harlow, Francis H. Computer Physics Communications, Vol. 48, Issue 1 https://doi.org/10.1016/0010-4655(88)90017-3	journal	January 1988
Heuristic stability theory for finite-difference equations Hirt, C. W. Journal of Computational Physics, Vol. 2, Issue 4 https://doi.org/10.1016/0021-9991(68)90041-7	journal	June 1968
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
Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux Noh, W. F. Journal of Computational Physics, Vol. 72, Issue 1 https://doi.org/10.1016/0021-9991(87)90074-X	journal	September 1987
Homogeneous difference schemes Tikhonov, A. N.; Samarskii, A. A. USSR Computational Mathematics and Mathematical Physics, Vol. 1, Issue 1 https://doi.org/10.1016/0041-5553(62)90005-8	journal	January 1962
A particle method for history-dependent materials Sulsky, D.; Chen, Z.; Schreyer, H. L. Computer Methods in Applied Mechanics and Engineering, Vol. 118, Issue 1-2 https://doi.org/10.1016/0045-7825(94)90112-0	journal	September 1994
Traveling wave solutions for finite scale equations Margolin, L. G.; Vaughan, D. E. Mechanics Research Communications, Vol. 45 https://doi.org/10.1016/j.mechrescom.2012.07.003	journal	October 2012
Kinematics of volume transport Brenner, Howard Physica A: Statistical Mechanics and its Applications, Vol. 349, Issue 1-2 https://doi.org/10.1016/j.physa.2004.10.033	journal	April 2005
Navier–Stokes revisited Brenner, Howard Physica A: Statistical Mechanics and its Applications, Vol. 349, Issue 1-2 https://doi.org/10.1016/j.physa.2004.10.034	journal	April 2005
Fluid mechanics revisited Brenner, Howard Physica A: Statistical Mechanics and its Applications, Vol. 370, Issue 2 https://doi.org/10.1016/j.physa.2006.03.066	journal	October 2006
Finite Volume Methods for Hyperbolic Problems LeVeque, Randall J. https://doi.org/10.1017/CBO9780511791253	book	January 2002
Advanced Transport Phenomena Leal, L. Gary Cambridge University Press https://doi.org/10.1017/CBO9780511800245	book	January 2007
The structure of shock waves as a test of Brenner's modifications to the Navier–Stokes equations Greenshields, Christopher J.; Reese, Jason M. Journal of Fluid Mechanics, Vol. 580 https://doi.org/10.1017/S0022112007005575	journal	May 2007
Electron beam density measurements in shock waves in argon Schmidt, B. Journal of Fluid Mechanics, Vol. 39, Issue 2 https://doi.org/10.1017/S0022112069002229	journal	November 1969
Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam Alsmeyer, H. Journal of Fluid Mechanics, Vol. 74, Issue 3 https://doi.org/10.1017/S0022112076001912	journal	April 1976
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
Note on Becker's Theory of the Shock Front Thomas, L. H. The Journal of Chemical Physics, Vol. 12, Issue 11 https://doi.org/10.1063/1.1723889	journal	November 1944
Kinetic approach to microscopic-macroscopic coupling in space and laboratory plasmas Lapenta, Giovanni; Brackbill, J. U.; Ricci, Paolo Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2173623	journal	May 2006
On the Origins of Lagrangian Hydrodynamic Methods Morgan, Nathaniel R.; Archer, Billy J. Nuclear Technology, Vol. 207, Issue sup1 https://doi.org/10.1080/00295450.2021.1913034	journal	November 2021
Richtmyer on Shocks “Proposed Numerical Method for Calculation of Shocks,” an Annotation of LA-671 Margolin, L. G.; van Buren, K. L. Fusion Science and Technology https://doi.org/10.1080/15361055.2023.2283660	journal	January 2024
Advances in petascale kinetic plasma simulation with VPIC and Roadrunner Bowers, K. J.; Albright, B. J.; Yin, L. Journal of Physics: Conference Series, Vol. 180 https://doi.org/10.1088/1742-6596/180/1/012055	journal	July 2009
The beginnings of applied mathematics after the Second World War Lax, Peter D. Quarterly of Applied Mathematics, Vol. 56, Issue 4 https://doi.org/10.1090/qam/1668731	journal	January 1998
Finite-scale equations for compressible fluid flow Margolin, L. G. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 367, Issue 1899 https://doi.org/10.1098/rsta.2008.0290	journal	July 2009
XV. On the thermodynamic theory of waves of finite longitudinal disturbance Macquorn Rankine, William John Philosophical Transactions of the Royal Society of London, Vol. 160, p. 277-288 https://doi.org/10.1098/rstl.1870.0015	journal	January 1870
Stigler'S law of Eponymy* Stigler, Stephen M. Transactions of the New York Academy of Sciences, Vol. 39, Issue 1 Series II https://doi.org/10.1111/j.2164-0947.1980.tb02775.x	journal	April 1980
Numerical Fluid Dynamics Birkhoff, Garrett SIAM Review, Vol. 25, Issue 1 https://doi.org/10.1137/1025001	journal	January 1983
A Numerical Method for Treating Fluid Flow in the Presence of Shocks Landshoff, R. https://doi.org/10.2172/4364774	report	January 1955

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