Asymptotical analysis of one dimensional gas dynamics equations

A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonanc...

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Main Authors: A. Krylovas, R. Čiegis
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2001-06-01
Series:Mathematical Modelling and Analysis
Subjects:
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Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/9890
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author A. Krylovas
R. Čiegis
author_facet A. Krylovas
R. Čiegis
author_sort A. Krylovas
collection DOAJ
description A method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given. Vienmačių dujų dinamikos lygčių asimptotinis sprendimo metodas Santrauka Darbe sukonstruotas asimptotinis skleidinys, kuris tolygiai aproksimuoja vienmačiu duju sprendini visame intervale t ≤ O(1/ϵ). Metodika remiasi anksčiau pasiūlytu lygčiu vidurkinimmo metodu. Surastos salygos, kada gautoji suvidurkinta diferencialiniu lygčiu sistema atsiskiria i tris nepriklausomas klampias Burgerso lygtis. Kai išpildytos rezonanso salygos, netiesiniu bangu saveika yra aprašoma integraliniais nariais. Pateiktos baigtiniu skirtumu schemos, aproksimuojančios tiek pradine diferencialiniu lygčiu sistema, tiek ir suvidurkintas lygtis. Atliktas skaičiavimo eksperimentas, patvirtinantis teorines išvadas. First Published Online: 14 Oct 2010
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spelling doaj.art-0d9074f6c20e4abebf2a78ca6989e86e2022-12-21T21:04:41ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102001-06-016110.3846/13926292.2001.9637151Asymptotical analysis of one dimensional gas dynamics equationsA. Krylovas0R. Čiegis1Vilnius Gediminas Technical University , Sauletekio al. 11, Vilnius, LT‐2040, LithuaniaVilnius Gediminas Technical University , Sauletekio al. 11, Vilnius, LT‐2040, LithuaniaA method of averaging is developed for constructing a uniformly valid asymptotic solution for weakly nonlinear one dimensional gas dynamics systems. Using this method we give the averaged system, which disintegrates into independent equations for the non‐resonance systems. Conditions of the resonance for periodic and almost periodic solutions are presented. In the resonance case the averaged system is solved numerically. Some results of numerical experiments are given. Vienmačių dujų dinamikos lygčių asimptotinis sprendimo metodas Santrauka Darbe sukonstruotas asimptotinis skleidinys, kuris tolygiai aproksimuoja vienmačiu duju sprendini visame intervale t ≤ O(1/ϵ). Metodika remiasi anksčiau pasiūlytu lygčiu vidurkinimmo metodu. Surastos salygos, kada gautoji suvidurkinta diferencialiniu lygčiu sistema atsiskiria i tris nepriklausomas klampias Burgerso lygtis. Kai išpildytos rezonanso salygos, netiesiniu bangu saveika yra aprašoma integraliniais nariais. Pateiktos baigtiniu skirtumu schemos, aproksimuojančios tiek pradine diferencialiniu lygčiu sistema, tiek ir suvidurkintas lygtis. Atliktas skaičiavimo eksperimentas, patvirtinantis teorines išvadas. First Published Online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/9890-
spellingShingle A. Krylovas
R. Čiegis
Asymptotical analysis of one dimensional gas dynamics equations
Mathematical Modelling and Analysis
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title Asymptotical analysis of one dimensional gas dynamics equations
title_full Asymptotical analysis of one dimensional gas dynamics equations
title_fullStr Asymptotical analysis of one dimensional gas dynamics equations
title_full_unstemmed Asymptotical analysis of one dimensional gas dynamics equations
title_short Asymptotical analysis of one dimensional gas dynamics equations
title_sort asymptotical analysis of one dimensional gas dynamics equations
topic -
url https://journals.vgtu.lt/index.php/MMA/article/view/9890
work_keys_str_mv AT akrylovas asymptoticalanalysisofonedimensionalgasdynamicsequations
AT rciegis asymptoticalanalysisofonedimensionalgasdynamicsequations