A Well-balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field

Volume 2, Issue 2

Kun Xu, Jun Luo & Songze Chen

DOI: 10.4208/aamm.09-m0964

Adv. Appl. Math. Mech., 2 (2010), pp. 200-210.

Published online: 2010-02

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Abstract

In this paper, a well-balanced kinetic scheme for the gas dynamic equations under gravitational field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface is considered, where the amount of particle penetration and reflection is evaluated according to the incident particle velocity. This work extends the approach of Perthame and Simeoni for the shallow water equations [Calcolo, 38 (2001), pp. 201-231] to the Euler equations under gravitational field. For an isolated system, this scheme is probably the only well-balanced method which can precisely preserve an isothermal steady state solution under time-independent gravitational potential. A few numerical examples are used to validate the above approach.

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@Article{AAMM-2-200, author = {}, title = {A Well-balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2010}, volume = {2}, number = {2}, pages = {200--210}, abstract = {In this paper, a well-balanced kinetic scheme for the gas dynamic equations under gravitational field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface is considered, where the amount of particle penetration and reflection is evaluated according to the incident particle velocity. This work extends the approach of Perthame and Simeoni for the shallow water equations [Calcolo, 38 (2001), pp. 201-231] to the Euler equations under gravitational field. For an isolated system, this scheme is probably the only well-balanced method which can precisely preserve an isothermal steady state solution under time-independent gravitational potential. A few numerical examples are used to validate the above approach.}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0964}, url = {http://global-sci.org/intro/article_detail/aamm/8327.html} }

TY - JOUR T1 - A Well-balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 200 EP - 210 PY - 2010 DA - 2010/02 SN - 2 DO - http://doi.org/10.4208/aamm.09-m0964 UR - https://global-sci.org/intro/article_detail/aamm/8327.html KW - AB - In this paper, a well-balanced kinetic scheme for the gas dynamic equations under gravitational field is developed. In order to construct such a scheme, the physical process of particles transport through a potential barrier at a cell interface is considered, where the amount of particle penetration and reflection is evaluated according to the incident particle velocity. This work extends the approach of Perthame and Simeoni for the shallow water equations [Calcolo, 38 (2001), pp. 201-231] to the Euler equations under gravitational field. For an isolated system, this scheme is probably the only well-balanced method which can precisely preserve an isothermal steady state solution under time-independent gravitational potential. A few numerical examples are used to validate the above approach.

Kun Xu, Jun Luo & Songze Chen. (1970). A Well-balanced Kinetic Scheme for Gas Dynamic Equations under Gravitational Field. Advances in Applied Mathematics and Mechanics. 2 (2). 200-210. doi:10.4208/aamm.09-m0964

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