The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state
A small viscosity approach to discontinuous flows is discussed in relativistic hydrodynamics with a general (possibly, non-convex) equation of state that typically occurs in the domains of phase transitions. Different forms of criteria for the existence and stability of relativistic shock waves,...
Збережено в:
| Дата: | 1998 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
1998
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/119812 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state / P.V. Tytarenko, V.I. Zhdanov // Condensed Matter Physics. — 1998. — Т. 1, № 3(15). — С. 643-654. — Бібліогр.: 15 назв. — англ. |
Репозитарії
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irk-123456789-1198122017-06-10T03:03:11Z The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state Tytarenko, P.V. Zhdanov, V.I. A small viscosity approach to discontinuous flows is discussed in relativistic hydrodynamics with a general (possibly, non-convex) equation of state that typically occurs in the domains of phase transitions. Different forms of criteria for the existence and stability of relativistic shock waves, such as evolutionarity conditions, entropy criterion and corrugation stability conditions are compared with the requirement of the existence of shock viscous profile. The latter is shown to be most restrictive in case of a single-valued shock adiabat expressed as a function of pressure. One-dimensional numerical simulations with artificial viscosity for a simple piecewise-linear equation of state are carried out to illustrate the criteria in the case of planar and spherical shock waves. The effect of a phase transition domain on the shock amplitude in the process of a hydrodynamical spherical collapse is demonstrated. Обговорюється підхід малої в’язкости до розривних потоків у релятивістичній гідродинаміці із загальним (можливо, неопуклим) рівнянням стану, яке характерне для области фазових переходів. Різні форми критеріїв існування та стійкости релятивістичних ударних хвиль — умови еволюційности, ентропійний критерій та умови складчастої стабільности — порівнюються з вимогою існування ударного в’язкісного профілю. Показано, що останній критерій є більш обмежуючим у випадку ударної адіябати, яка виражається як однозначна функція тиску. Для ілюстрування цих критеріїв у випадку плоских та сферичних ударних хвиль проведено одновимірне числове моделювання зі штучною в’язкістю для простого кусково–лінійного рівняння стану. Продемонстровано вплив области фазових переходів на ударну амплітуду у процесі гідродинамічного сферичного колапсу. 1998 Article The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state / P.V. Tytarenko, V.I. Zhdanov // Condensed Matter Physics. — 1998. — Т. 1, № 3(15). — С. 643-654. — Бібліогр.: 15 назв. — англ. 1607-324X DOI:10.5488/CMP.1.3.643 PACS: 95.30.Lz, 95.30.Qd http://dspace.nbuv.gov.ua/handle/123456789/119812 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A small viscosity approach to discontinuous flows is discussed in relativistic
hydrodynamics with a general (possibly, non-convex) equation of state
that typically occurs in the domains of phase transitions. Different forms of
criteria for the existence and stability of relativistic shock waves, such as
evolutionarity conditions, entropy criterion and corrugation stability conditions
are compared with the requirement of the existence of shock viscous
profile. The latter is shown to be most restrictive in case of a single-valued
shock adiabat expressed as a function of pressure. One-dimensional numerical
simulations with artificial viscosity for a simple piecewise-linear
equation of state are carried out to illustrate the criteria in the case of planar
and spherical shock waves. The effect of a phase transition domain on
the shock amplitude in the process of a hydrodynamical spherical collapse
is demonstrated. |
| format |
Article |
| author |
Tytarenko, P.V. Zhdanov, V.I. |
| spellingShingle |
Tytarenko, P.V. Zhdanov, V.I. The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state Condensed Matter Physics |
| author_facet |
Tytarenko, P.V. Zhdanov, V.I. |
| author_sort |
Tytarenko, P.V. |
| title |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| title_short |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| title_full |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| title_fullStr |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| title_full_unstemmed |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| title_sort |
existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1998 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119812 |
| citation_txt |
The existence and stability of relativistic shock waves: general criteria and numerical simulations for a non-convex equation of state / P.V. Tytarenko, V.I. Zhdanov // Condensed Matter Physics. — 1998. — Т. 1, № 3(15). — С. 643-654. — Бібліогр.: 15 назв. — англ. |
| series |
Condensed Matter Physics |
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