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One-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates: symmetry classification, conservation laws, difference schemes

V.A. Dorodnitsyn, R. Kozlov, S.V. Meleshko
2019 Communications in nonlinear science & numerical simulation  
Lie point symmetries of the one-dimensional gas dynamics equations of a polytropic gas in Lagrangian coordinates are considered.  ...  Noether theorem is applied for constructing conservation laws. The conservation laws can be represented in the gas dynamics variables.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant No 18-11-00238 'Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes'.  ... 
doi:10.1016/j.cnsns.2019.03.009 fatcat:zzpnkxqsenhapcssrqs5ailhgy

Conservation Laws of One-Dimensional Equations of Relativistic Gas Dynamics in Lagrangian Coordinates [article]

Warisa Nakpim, Sergey V. Meleshko
2019 arXiv   pre-print
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations.  ...  The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas dynamics equations can be rewritten in a variational form.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant No 18-11-00238 'Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes'.  ... 
arXiv:1912.12496v1 fatcat:yxgnvy25nrauvfgqss6tlkspdy

One-dimensional flows of a polytropic gas: Lie group classification, conservation laws, invariant and conservative difference schemes [article]

Vladimir A. Dorodnitsyn, Roman Kozlov, Sergey V. Meleshko
2020 arXiv   pre-print
The one-dimensional flow of a polytropic gas is described by one second-order partial differential equation in the Lagrangian variables. Lie group classification of this PDE is performed.  ...  These conservation laws are also recalculated for the gas dynamics variables in the Lagrangian and Eulerian coordinates. Additionally, invariant and conservative difference schemes are provided.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant no. 18-11-00238 "Hydrodynamicstype equations: symmetries, conservation laws, invariant difference schemes".  ... 
arXiv:2011.14397v1 fatcat:eyrsnpvy7ffwpedlbfudtukila

Shallow water equations in Lagrangian coordinates: symmetries, conservation laws and its preservation in difference models [article]

V.A. Dorodnitsyn, E.I. Kaptsov
2019 arXiv   pre-print
The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered.  ...  For equations in Lagrangian coordinates with a flat bottom an invariant difference scheme is constructed which possesses all the difference analogues of the conservation laws: mass, momentum, energy, the  ...  Acknowledgements The research was supported by Russian Science Foundation Grant No 18-11-00238 'Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes'.  ... 
arXiv:1912.13314v1 fatcat:3u5kkbzduba3thdskqjlfv6xf4

Conservation Laws of the Two-Dimensional Gas Dynamics Equations [article]

E.I. Kaptsov, S.V. Meleshko
2018 arXiv   pre-print
Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations.  ...  Using group classification and Noether's theorem, conservation laws are obtained. Their counterparts in Eulerian coordinates are given. Among these counterparts there are new conservation laws.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant No 18-11-00238 'Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes'.  ... 
arXiv:1812.04301v1 fatcat:uc5hgikijvakzfcnwhdg5ju3pe

Invariant Finite-Difference Schemes for Plane One-Dimensional MHD Flows That Preserve Conservation Laws

Vladimir Dorodnitsyn, Evgeniy Kaptsov
2022 Mathematics  
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity.  ...  This is achieved by means of specially selected approximations for the equation of state of a polytropic gas. In addition, invariant difference schemes with additional conservation laws are proposed.  ...  E.K. sincerely appreciates the hospitality of the Suranaree University of Technology. Conflicts of Interest: The authors declare no conflicts of interest.  ... 
doi:10.3390/math10081250 fatcat:6s4urhxhjjdcjhlrcqewyrapai

Invariant finite-difference schemes with conservation laws preservation for one-dimensional MHD equations [article]

E. I. Kaptsov, V. A. Dorodnitsyn
2022 arXiv   pre-print
Invariant finite-difference schemes are considered for one-dimensional magnetohydrodynamics (MHD) equations in mass Lagrangian coordinates for the cases of finite and infinite conductivity.  ...  For isentropic flows of a polytropic gas proposed schemes possess the conservation law of energy and preserve entropy on two time layers.  ...  E.K. sincerely appreciates the hospitality of the Suranaree University of Technology. Conflicts of Interest: The authors declare no conflict of interest.  ... 
arXiv:2112.03118v2 fatcat:supckwakorf6fpdgzulcen24pu

Invariant Solutions of the Two-Dimensional Shallow Water Equations with a Particular Class of Bottoms [article]

S.V. Meleshko, N.F. Samatova
2020 arXiv   pre-print
The two-dimensional shallow water equations with a particular bottom and the Coriolis's force f=f_0+Ω y are studied in this paper.  ...  The main goal of the paper is to describe all invariant solutions for which the reduced system is a system of ordinary differential equations.  ...  ACKNOWLEDGEMENTS The research was supported by Russian Science Foundation Grant No 18-11-00238 'Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes'.  ... 
arXiv:2001.03109v1 fatcat:722pmmmawbfrjco6fe27lkexyy

Plane one-dimensional MHD flows: symmetries and conservation laws [article]

Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman V. Kozlov, Sergey V. Meleshko, Potcharapol Mukdasanit
2021 arXiv   pre-print
The paper considers the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. The inviscid, thermally non-conducting medium is modeled by a polytropic gas.  ...  The conservation laws are derived by the direct computation. For the case of the infinite electrical conductivity the equations can be brought into a variational form in the Lagrangian coordinates.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant no. 18-11-00238 "Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes".  ... 
arXiv:2110.08235v2 fatcat:qv5f5vv7xrhzrdrcjcrnv5unga

One-dimensional MHD flows with cylindrical symmetry: Lie symmetries and conservation laws [article]

Vladimir A. Dorodnitsyn, Evgeniy I. Kaptsov, Roman V. Kozlov, Sergey V. Meleshko
2022 arXiv   pre-print
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates.  ...  It is modeled by a polytropic gas. Symmetries and conservation laws are found. The cases of finite and infinite electric conductivity need to be analyzed separately.  ...  Acknowledgements The research was supported by Russian Science Foundation Grant no. 18-11-00238 "Hydrodynamics-type equations: symmetries, conservation laws, invariant difference schemes".  ... 
arXiv:2207.05379v1 fatcat:fkpdax5onvg7jhqrpepulonbpe

The radial structure of galaxy groups and clusters

Y. Ascasibar, G. Yepes, V. Müller, S. Gottlöber
2003 Monthly notices of the Royal Astronomical Society  
The hot X-ray emitting gas is found to be in approximate hydrostatic equilibrium with the dark matter potential, and it is well described by a polytropic equation of state.  ...  Numerical resolution and entropy conservation play a key role in the shapes of the profiles at small radii.  ...  In part inspired by the success of the N-body scheme, the first gas-dynamical techniques were based on a particle representation of Lagrangian gas elements using the SPH technique (Lucy 1977; Gingold  ... 
doi:10.1111/j.1365-2966.2003.07116.x fatcat:7eczvuvmhjgvnexoqmlekchkmi

Symmetries of Differential Equations in Cosmology [article]

Michael Tsamparlis, Andronikos Paliathanasis
2018 arXiv   pre-print
The purpose of the current article is to present a brief albeit accurate presentation of the main tools used in the study of symmetries of Lagrange equations for holonomic systems and subsequently to show  ...  By means of the Inverse Noether Theorem we show that to every Hojman quadratic first integral one is possible to associate a Noether symmetry whose Noether integral is the original Hojman integral.  ...  Acknowledgement AP acknowledges financial support of FONDECYT grant no. 3160121  ... 
arXiv:1806.05888v1 fatcat:6vzovs5mozcrzdjxrbslvqd22e

Perturbation analysis of a general polytropic homologously collapsing stellar core

Yi Cao, Yu-Qing Lou
2009 Monthly notices of the Royal Astronomical Society  
For dynamic background models of Goldreich & Weber and Lou & Cao, we examine 3-dimensional perturbation properties of oscillations and instabilities in a general polytropic homologously collapsing stellar  ...  core of a relativistic hot medium with a polytropic index of 4/3.  ...  This research was supported in part by Tsinghua Centre for Astrophysics (THCA), by the National Natural Science Foundation of China (NSFC) grants 10373009 and 10533020 at Tsinghua University, and by the  ... 
doi:10.1111/j.1365-2966.2009.15597.x fatcat:hurzrk7exndydju6zgx3cyz4bu

Nonlinear dispersive regularization of inviscid gas dynamics [article]

Govind S Krishnaswami, Sachin Phatak, Sonakshi Sachdev, A Thyagaraja
2019 arXiv   pre-print
Here, we develop a minimal conservative regularization of 3d ideal adiabatic flow of a gas with polytropic exponent γ.  ...  Thus, our regularization of gas dynamics may be viewed as a generalization of both the single field KdV NLS equations to include the adiabatic dynamics of density, velocity, pressure entropy in any dimension  ...  This work was supported in part by the Infosys Foundation, J N Tata Trust and the Science and Engineering Research Board, Govt. of India via grant CRG/2018/002040.  ... 
arXiv:1910.07836v1 fatcat:3s4i3l2arjhj3pvpqaavugfr34

Nonlinear dispersive regularization of inviscid gas dynamics

Govind S. Krishnaswami, Sachin S. Phatak, Sonakshi Sachdev, A. Thyagaraja
2020 AIP Advances  
FORMULATION OF ONE-DIMENSIONAL REGULARIZED GAS DYNAMICS A.  ...  VI, a semi-implicit spectral numerical scheme for the isentropic R-gas dynamic equations with periodic boundary conditions (BCs) in one dimension.  ... 
doi:10.1063/1.5133720 fatcat:xhnixxhgwremtn2auazrzh2u2y
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