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 resonan...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2001-06-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/9890 |
| Summary: | 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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| ISSN: | 1392-6292 1648-3510 |