Top

Fluid Dynamics

Published in:

01-02-2023

Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe

Authors: A. V. Aksenov, K. P. Druzhkov

Published in: Fluid Dynamics | Issue 1/2023

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

The system of equations that describes one-dimensional polytropic gas flows is considered. The invariants up to the second order of characteristics of the considered system of equations are classified. The method of reducing the Cauchy problems to systems of ordinary differential equations is proposed. Examples of the solutions without gradient catastrophe are constructed using invariants of characteristics supplementary to the Riemann invariants.

previous article Lift Airfoils Close to the Airfoils in a Flow with the Maximum “Critical” Mach Numbers

next article Formation of Shock-Wave Flow during Nanosecond Discharge Localization in Unsteady Flow in a Channel with Obstacles

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Riemann, B., Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Aus dem achten Bande der Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematischphysikalische Klasse, 1860, Band 8, Nr. 43, S. 43–66. [Retrieved from https://eudml.org/doc/135717].

Darboux, M.G., Sur la théorie des équations aux dérivos partielles du second ordre, Comptes rendus hebdomadaires des séances de l’Académie des sciences Paris, 1870, vol. 70, pp. 675–678.

Darboux, M.G., Sur la théorie des équations aux dérivos partielles, Comptes rendus hebdomadaires des séances de l’Académie des sciences Paris, 1870, vol. 70, pp. 746–749.

Goursat, M.E., Leçons sur l’intégration des équations aux deroves partielles du second order a deux variables indépendantes, Tome II, Paris: 1898 (Librairie scientifique A. Hermann).

Kaptsov, O.V., Metody integrirovaniya uravnenii s chastnymi proizvodnymi (Methods of Integation of Partial Differential Equations), Moscow: FIZMATLIT, 2009.

Aksenov, A.V., Nonlinear periodic waves in a gas, Fluid Dyn., 2012, vol. 47, no. 5, pp. 636–646.https://doi.org/10.1134/S0015462812050110ADSMathSciNetCrossRefMATH

Rozhdestvenskii, B.L. and Yanenko, N.N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike (Systems of Quasi-Linear Equations and Their Applications to Gas Dynamics), Moscow: Nauka, 1978.

Aksenov, A.V., Druzhkov, K.P., and Kaptsov, O.V., Application of invariants of characteristics to construction of solutions without gradient catastrophe, Int. J. Non-Linear Mechanics, 2022, vol. 147, no. 104249, pp. 1–8.CrossRef

Title: Construction of Exact Solutions of the System of One-Dimensional Gas Dynamics Equations without Gradient Catastrophe
Authors: A. V. Aksenov
K. P. Druzhkov
Publication date: 01-02-2023
Publisher: Pleiades Publishing
Published in: Fluid Dynamics / Issue 1/2023
Print ISSN: 0015-4628
Electronic ISSN: 1573-8507
DOI: https://doi.org/10.1134/S0015462822601899

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 1/2023

Using the Wave Propulsors in a Small-Waterplane-Area-Twin-Hull Boat

Effect of Confinement of Flow by Side Walls on the Cross Flow past a Circular Cylinder at Moderate Reynolds Numbers

Effect of Particle Thermophoresis on Convection of Magnetic Fluids in Narrow Channels Heated from Below

Motion of a Piston Separating Magnetic and Non-Magnetic Fluids in a Magnetic Field

Duality of the Stream Pattern of Supersonic Viscous Gas Flow past a Blunt-Fin Junction: the Effect of a Low Sweep Angle

Mass Transfer from a Drop in Fall into the Fluid Thickness in the Initial Stage of the Coalescence Process

Premium Partners