Symmetries of the Gas Dynamics Equations using the Differential Form Method
Abstract
A brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators—and corresponding EOS constraints—otherwise appearing in the existing literature are recovered through the application and invariance under Lie derivative dragging operations.
- Authors:
-
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1418762
- Alternate Identifier(s):
- OSTI ID: 1409706
- Report Number(s):
- LA-UR-16-29415
Journal ID: ISSN 0022-2488; 1089-7658 (Electronic); TRN: US1801297
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Mathematical Physics
- Additional Journal Information:
- Journal Volume: 58; Journal Issue: 11; Journal ID: ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Fluid flows; Differential geometry; Bulk modulus; Equations of state; Fluid
Citation Formats
Ramsey, Scott D., and Baty, Roy S. Symmetries of the Gas Dynamics Equations using the Differential Form Method. United States: N. p., 2017.
Web. doi:10.1063/1.5011723.
Ramsey, Scott D., & Baty, Roy S. Symmetries of the Gas Dynamics Equations using the Differential Form Method. United States. https://doi.org/10.1063/1.5011723
Ramsey, Scott D., and Baty, Roy S. Tue .
"Symmetries of the Gas Dynamics Equations using the Differential Form Method". United States. https://doi.org/10.1063/1.5011723. https://www.osti.gov/servlets/purl/1418762.
@article{osti_1418762,
title = {Symmetries of the Gas Dynamics Equations using the Differential Form Method},
author = {Ramsey, Scott D. and Baty, Roy S.},
abstractNote = {A brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators—and corresponding EOS constraints—otherwise appearing in the existing literature are recovered through the application and invariance under Lie derivative dragging operations.},
doi = {10.1063/1.5011723},
journal = {Journal of Mathematical Physics},
number = 11,
volume = 58,
place = {United States},
year = {Tue Nov 21 00:00:00 EST 2017},
month = {Tue Nov 21 00:00:00 EST 2017}
}
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Works referenced in this record:
Numerical Method for Darcy Flow Derived Using Discrete Exterior Calculus
journal, May 2015
- Hirani, A. N.; Nakshatrala, K. B.; Chaudhry, J. H.
- International Journal for Computational Methods in Engineering Science and Mechanics, Vol. 16, Issue 3
Geometric Approach to Invariance Groups and Solution of Partial Differential Systems
journal, April 1971
- Harrison, B. Kent; Estabrook, Frank B.
- Journal of Mathematical Physics, Vol. 12, Issue 4
Analytic solutions of hydrodynamics equations
journal, May 1991
- Coggeshall, S. V.
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 5
Exterior differential systems and prolongations for three important nonlinear partial differential equations
journal, April 2011
- Bracken, Paul
- Communications on Pure and Applied Analysis, Vol. 10, Issue 5
A finite element exterior calculus framework for the rotating shallow-water equations
journal, January 2014
- Cotter, C. J.; Thuburn, J.
- Journal of Computational Physics, Vol. 257
Solutions of the Noh problem for various equations of state using LIE groups
journal, January 2000
- Axford, Roy A.
- Laser and Particle Beams, Vol. 18, Issue 1
Converging finite-strength shocks
journal, January 1981
- Axford, R. A.; Holm, D. D.
- Physica D: Nonlinear Phenomena, Vol. 2, Issue 1
The Differential Form Method for Finding Symmetries
journal, August 2005
- Harrison, B. Kent
- Symmetry, Integrability and Geometry: Methods and Applications
An Exterior Differential System for a Generalized Korteweg-de Vries Equation and its Associated Integrability
journal, March 2007
- Bracken, Paul
- Acta Applicandae Mathematicae, Vol. 95, Issue 3
Group‐invariant solutions and optimal systems for multidimensional hydrodynamics
journal, October 1992
- Coggeshall, S. V.; Meyer‐ter‐Vehn, J.
- Journal of Mathematical Physics, Vol. 33, Issue 10
Structure-preserving discretization of incompressible fluids
journal, March 2011
- Pavlov, D.; Mullen, P.; Tong, Y.
- Physica D: Nonlinear Phenomena, Vol. 240, Issue 6
The Riemann problem for fluid flow of real materials
journal, January 1989
- Menikoff, Ralph; Plohr, Bradley J.
- Reviews of Modern Physics, Vol. 61, Issue 1
Prolongation structures of nonlinear evolution equations
journal, January 1975
- Wahlquist, H. D.; Estabrook, F. B.
- Journal of Mathematical Physics, Vol. 16, Issue 1
Works referencing / citing this record:
Piston driven converging shock waves in a stiffened gas
journal, August 2019
- Ramsey, Scott D.; Baty, Roy S.
- Physics of Fluids, Vol. 31, Issue 8