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In this paper, we recount the history of artificial viscosity, beginning with its origin in previously unpublished and unavailable documents, continuing on to current research and ending with recent work describing its physical basis that suggests new directions for improvement.
Lord Rayleigh, Aerial plane waves of finite amplitude, Proc. R. Soc. Lond. Ser. A 84 (1910) 247–284
1910
Earlier work this paper cites.
G.I.Taylor,The conditions necessary for discontinuous motion in gases, Proc. R. Soc. Lond. Ser. A 84 (1910) 371–377
1910
Earlier work this paper cites.
R. Becker, 1922: “Stoßbwelle und detonation,” (In German), Zeitschrift für Physik 8
1922
Earlier work this paper cites.
R. Landshoff, 1955: “A numerical method for treating fluid flow in the presence of shocks,” Los Alamos Scientific Laboratory Report LA-1930
1930
Earlier work this paper cites.
J. von Neumann & R.D. Richtmyer, 1947: “On the numerical solution of partial differential equations of parabolic type,” Los Alamos Scientific Laboratory Report LA-657, 1–17
1947
Earlier work this paper cites.
R. Peierls, 1948: “Letter to J. von Neumann, March, 1948,” reproduced in Los Alamos National Laboratory report LA-UR-20-28408
1948
Earlier work this paper cites.
M. Morduchow & P.A. Libby, 1949: “On a complete solution of the one–dimensional flow equations of a viscous, heat–conducting, compressible gas,” J. Aeronautical Sciences 16
1949
Earlier work this paper cites.
J. von Neumann & R.D. Richtmyer, 1950: “A method for the numerical calculation of hydrodynamic shocks,” J. Appl. Phys. 21
1950
Earlier work this paper cites.
P.D. Lax, 1952: “On discontinuous initial value problems for nonlinear equations and finite differences,” Los Alamos Scientific Laboratory Report LAMS–1332
1952
Earlier work this paper cites.
S.K. Godunov, 1954, Ph.D. Dissertation: Difference Methods for Shock Waves, Moscow State University
1954
Earlier work this paper cites.
H.G. Kolsky, 1955: “A method for the numerical solution of transient hydrodynamic shock problems in two space dimensions,” Los Alamos Scientific Laboratory Report LA-1867
1955
Earlier work this paper cites.
B. Alder, S. Fernbach & M. Rottenberg, eds., Methods in Computational Physica, Vol. 3
1964
Earlier work this paper cites.
F. Schultz–Grunow & A. Frohn, 1965: “Density distribution in shock waves traveling in rarefied gases,” in Rarefied Gas Dynamics
1965
Earlier work this paper cites.
C.W. Hirt, 1968: “Heuristic stability theory for finite difference equations. J. Comput. Phys. 2
1968
Earlier work this paper cites.
B. Schmidt, 1969: “Electron beam density measurements in shock waves in argon,” J. Fluid Mech. 39
1969
Earlier work this paper cites.
H. Goldstine, The Computer from Pascal to von Neumann
1972
Earlier work this paper cites.
P.A. Thompson, Compressible-Fluid Dynamics
1972
Earlier work this paper cites.
Boris, JP, Book, DL., 1973: ”Flux-corrected transport: 1. SHASTA, A fluid transport algorithm that works,” J. Comput. Phys. 11
1973
Earlier work this paper cites.
H. Alsmeyer, 1976: “Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam,” J. Fluid Mech. 74
1976
Earlier work this paper cites.
1980
Earlier work this paper cites.
L. R. Groves, Now It Can Be Told
1983
Earlier work this paper cites.
P.K. Sweby, 1984: “High resolution schemes using flux limiters for hyperbolic conserrvation laws,” SIAM J. Numewr. Anal., 21
1984
Earlier work this paper cites.
L.G. Margolin & T. F. Adams, 1985:“Spatial differencing for finite difference codes,” Los Alamos National Laborratory report LA-10249
1985
Earlier work this paper cites.
L.G. Margolin, H.M. Ruppel & R.B. Demuth, 1985: “Gradient scaling for nonuniform meshes,” Proc. Fourth International Conference on Numerical Methods in Laminar and Turbulent Flow, University of Wales, Swansea, UK, July 9–12, 1985, 1477–1488
1985
Earlier work this paper cites.
M.L. Merriam, 1987: ”Smoothing and the Second Law,” Comp. Meth. Appl. Mech. Eng. 64
1987
Cited alongside, same era.
W.F. Noh, 1987: “Errors for calculations of strong shocks using an artificial viscosity and an artificial heat conduction,” J. Comput. Phys. 72
1987
Cited alongside, same era.
L.G. Margolin, 1988:“A centered artificial viscosity for cells with large aspect ratio,” Lawrence Livermore Report UCRL-53882
1988
Cited alongside, same era.
R.B. Christiansen, Godunov methods on a staggered mesh: An improved artificial viscosity
1990
Cited alongside, same era.
C. Foias, O. Manley & R. Temam, 1991: “Approximate inertial manifolds and effective viscosity in turbulent flows,” Phys. Fluids A 3
1991
Cited alongside, same era.
H. Brenner, 2009: “Bi–velocity hydrodynamics: single–component fluids,” Int. J. Engin. Science 47
2009
Later among the works it cites.
L.G. Margolin, 2009: “Finite-scale equations for compressible fluid flow,” Phil. Trans. R. Soc. A 367
2009
Later among the works it cites.
G.M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases
2010
Later among the works it cites.
R. Loubére, P. Maire, & P. Vachal, 2011: “3D staggered Lagrangian hydrodynamics with cell–centered Riemann solver–based artificial viscosity, Int. J. Numer. Methods Fluids 72
2011
Later among the works it cites.
L.G. Margolin & D.E. Vaughan, 2012: “Traveling wave solutions for finite scale equations,” Mech. Res. Comm. 45
2012
Later among the works it cites.
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1994
Cited alongside, same era.
U. Frisch, Turbulence, The Legacy of A. N. Kolmogorov
1995
Cited alongside, same era.
M. Shashkov, Conservative Finite-difference Methods on General Grids
1996
Cited alongside, same era.
E.C. Caramana, M.J. Shashkov & P.P. Whalen, 1998: “Formulations of artificial viscosity for multi–dimensional shock wave computations,” J. Comp. Phys. 144
1998
Cited alongside, same era.
J.N. Johnson & R. Chéret, Classic Papers in Shock Compression Science
1998
Cited alongside, same era.
P.K. Smolarkiewicz & L.G. Margolin, 1998: “MPDATA: a finite difference solver for geophysical flows,” J. Comput. Phys. 149
1998
Cited alongside, same era.
S. B Pope (2000). Turbulent Flows
2000
Cited alongside, same era.
J.P. Boris, 2013: ”Flux-corrected transport looks at forty,” Computers & Fluids 84
2013
Later among the works it cites.
N.R. Morgan, 2013: “A dissipation model for staggered grid Lagrangian hydrodynamics,” Cmputers & Fluids 83
2013
Later among the works it cites.
J. Reisner, J. Serencsa & S. Shkoller, 2013: “ A space–time smooth artificial viscosity method for nonlinear conservation laws,” J. Comput. Phys. 235
2013
Later among the works it cites.
L.G. Margolin, 2014: “Finite scale theory: the role of the observer in classical fluid flow,” Mech. Res. Comm. 57
2014
Later among the works it cites.
N.R. Morgan, K.N.Lipnikov, D.E. Burton, & M.A. Kenamond, 2014: “A Lagrangian staggered grid Godunov–like approach for hydrodynamics,” J. Comput. Phys. 259
2014
Later among the works it cites.
A.E. Mattsson & W.J. Rider, 2015: “Artificial viscosity: back to basics,” Int. J. Num. Meth. Fluids 77
2015
Later among the works it cites.
L.G. Margolin, J.M. Reisner & P.M. Jordan, 2017: “Entropy in self-similar shock profiles,” Int. J. Nonlinear Mech. 95
2017
Later among the works it cites.
S.D. Ramsey, Z.M. Boyd & S.C. Burnett, 2017: “Solution of the Noh problem using the universal symmetry of the gas dynamics equations, Shock Waves 27
2017
Later among the works it cites.
L.G. Margolin, 2018: “Scale matters,” Phil. Trans. R. Soc. A 376
2018
Later among the works it cites.
L.G. Margolin & A. Hunter, 2018: “Discrete thermodynamics”, Mech. Research Comm. 93
2018
Later among the works it cites.
A.L. Velikovich, J.L. Guiliani & S.T. Zalesak, 2018: “Generalized Noh self–similar solutions of the compressible Euler equations for hydrocode verification J. Comput. Phys. 374
2018
Later among the works it cites.
L.G. Margolin, 2019: “The reality of artificial viscosity,” Shock Waves 29
2019
Later among the works it cites.
L.G. Margolin & C.S. Plesko, 2019: “Discrete regularization,” Evolution Equations and Control Theory 8
2019
Later among the works it cites.
J. Albright & M. Shashkov, 2020: “Locally adaptive artificial viscosity strategies for Lagrangian hydrodynamics,” Computers and Fluids 205
2020
Later among the works it cites.
L.G. Margolin, C.S. Plesko & J.M. Reisner, 2020: “A finite scale model for shock structure,” Phys. D 403
2020
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L.G. Margolin, C.S. Plesko & J.M. Reisner, 2020: “Finite scale theory: predicting nature’s shocks,” Wave Motion 98
2020
Later among the works it cites.
N.R. Morgan & B.J. Archer, 2021: “On the origins of Lagrangian hydrodynamic methods,” Los Alamos National Laboratory report LA-UR-21-20144
2021
Later among the works it cites.
L.G. Margolin & S.D. Ramsey, “Structure Functions for Numerical Shocks,” to appear In: Numerical Fluid Dynamics: Methods & Computations
2022
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