## A Mathematical Model of the Passage of an Asteroid-Comet Body through the Earth's Atmosphere

Тип публикации: доклад, тезисы доклада, статья из сборника материалов конференций

Конференция: International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS); Albena, BULGARIA; Albena, BULGARIA

Год издания: 2015

Идентификатор DOI: 10.1063/1.4934284

Ключевые слова: Time-dependent Navier-Stokes equations, viscous heat-conducting gas, friable asteroid-comet body, ionization and decomposition of molecules, semi-Lagrangian approximation, conforming finite element method

Аннотация: In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth's atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.

#### Издание

Журнал: APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES (AMITANS'15)

Выпуск журнала: Vol. 1684

ISSN журнала: 0094243X

Место издания: MELVILLE

Издатель: AMER INST PHYSICS

#### Авторы

• Shaydurov V. (SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia; Siberian Fed Univ, Krasnoyarsk 660041, Russia)
• Shchepanovskaya G. (SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia)
• Yakubovich M. (SB RAS, Inst Computat Modeling, Krasnoyarsk 660036, Russia)

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