Geometric Study of Gas Behavior in a One-Dimensional Nozzle (the Case of the van Der Waals Gas)

I. S. Krasil’shchik, Valentin Lychagin

Type: Article

Publication Date: 2020-12-01

Citations: 0

DOI: https://doi.org/10.1134/s1995080220120185

Abstract

We construct a three-component system of PDEs describing dynamics of van der Walls gas in one-dimensional nozzle. The group of conservation laws for this system is described. We also compute the Lie algebras of point symmetries and present group classification. Examples of exact invariant solutions are given.

Locations

Lobachevskii Journal of Mathematics - View
arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+	Geometric study of gas behavior in a one-dimensional nozzle (the case of the van der Waals gas	2020	I. S. Krasil’shchik Valentin Lychagin
+	Evolution of weak discontinuity in a van der Waals gas	2015	B. Bira T. Raja Sekhar
+	Group analysis of three dimensional Euler equations of gas dynamics	2009	Mehdi Nadjafikhah
+	Group-Theoretical Classification of Equations Describing One-Dimensional Nonsteady Gas Flows	1964	K. P. Surovikhin
+	On Lie symmetry mechanics for Navier–Stokes equations unified with non-Newtonian fluid model: A classical directory	2019	Khalil Ur Rehman M.Y. Malik
+	Symmetric Solutions for System of unsteady flow of a polytropic gas	2016	Hassan A. Zedan M. Abo-Zaid
+	Group Analysis of the One-Dimensional Gas Dynamics Equations in Lagrangian Coordinates and Conservation Laws	2020	Chompit Kaewmanee Sergey V. Meleshko
+	Group classification of equations of motion of a gas in a constant force field	1996	Sergey V. Meleshko
+ PDF Chat	One-Dimensional Flows of a Polytropic Gas: Lie Group Classification, Conservation Laws, Invariant and Conservative Difference Schemes	2021	В. А. Дородницын Roman Kozlov Sergey V. Meleshko
+ PDF Chat	Lie symmetry analysis and invariant solutions of $$\varvec{(3+1)}$$ ( 3 + 1 ) -dimensional Calogero–Bogoyavlenskii–Schiff equation	2018	Vishakha Jadaun Sachin Kumar
+ PDF Chat	A Group Classification of a System of Partial Differential Equations Modeling Flow in Collapsible Tubes	2009	Motlatsi Molati F. M. Mahomed C. Wafo Soh
+ PDF Chat	Special Issue on Symmetry and Fluid Mechanics	2020	R. Ellahi
+	Lie symmetry analysis, new group invariant for the (3 + 1)-dimensional and variable coefficients for liquids with gas bubbles models	2021	Mohamed R. Ali R. Sadat
+	On Infinite-dimensional Lie Algebra of Navier–Stokes Equation and Conservation Laws	2023	Manjit Singh
+	Lie Symmetry Method for Solutions of Differential Equations with Applications in Physics	2015	S. Reza Hejazi Elaheh Saberi Paeezeh Mahdavi
+	Group classification of the equations of two-dimensional motions of a gas	1994	Sergey V. Meleshko
+	Conservation equations of gasdynamics in curvilinear coordinate systems	1974	Marcel Vinokur
+	Three dimensional Motion of Gas	1960	K. P. Stanyukovich
+ PDF Chat	Symmetry Reductions and Exact Solutions of the (2+1)-Dimensional Navier-Stokes Equations	2010	Xiaorui Hua Zhongzhou Dongb Fei Huangc Yong Chena
+	Algebraic self-modeling solutions of two-dimensional transonic gas flow	1966	S. V. Fal'kovich Ilya Chernov

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (7)

Action	Title	Year	Authors
+	Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena	1985	Valentin Lychagin
+	Group Analysis of Differential Equations.	1985	Willard Miller Л.В. Овсянников
+	Contact Geometry and Non-linear Differential Equations	2006	Alexei Kushner Valentin Lychagin Vladimir Rubtsov
+	Critical Phenomena in Filtration Processes of Real Gases	2020	Valentin Lychagin Mikhail Roop
+	Symmetries and Conservation Laws for Differential Equations of Mathematical Physics	1999	A. Bocharov В. Н. Четвериков S. Duzhin Н. Г. Хорькова Alexey Samokhin Yu. Torkhov Alexander Verbovetsky
+	A. Kushner, V. Lychagin and V. Rubtsov: Contact Geometry and Non-linear Differential Equations, Encyclopedia Math. Appl., 101, Cambridge Univ. Press, 2007年，xxii + 496ページ．	2009	佐藤肇
+	Blow-Up in Nonlinear Equations of Mathematical Physics	2018	М. О. Корпусов Alexey Ovchinnikov А.Г. Свешников E. V. Yushkov