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Gas Kinetic Scheme for Anisotropic Savage-Hutter Model

Published online by Cambridge University Press:  03 June 2015

Wen-Chi Chen ,
Chih-Yu Kuo ,
Keh-Ming Shyue  and
Yih-Chin Tai
Wen-Chi Chen*
Affiliation:
Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan
Chih-Yu Kuo*
Affiliation:
Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan
Keh-Ming Shyue*
Affiliation:
Department of Mathematics, National Taiwan University, Taipei 106, Taiwan
Yih-Chin Tai*
Affiliation:
Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
*
Email:olivech@gate.sinica.edu.tw
Corresponding author.Email:cykuo06@gate.sinica.edu.tw
Email:shyue@math.ntu.edu.tw
Email:yctai@mail.ncku.edu.tw
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Abstract

The gas-kinetic scheme is applied to a depth-integrated continuum model for avalanche flows, namely the Savage-Hutter model. In this method, the continuum fluxes are calculated based on the pseudo particle motions which are relaxed from nonequilibrium to equilibrium states. The processes are described by the Bhatnagar-Gross-Krook (BGK) equation. The benefit of this scheme is its capability to resolve shock discontinuities sharply and to handle the vacuum state without special treatments. Because the Savage-Hutter equation bears an anisotropic stress on the tangential space of the topography, the equilibrium distribution function of the microscopic particles are shown to be bi-Maxwellian. These anisotropic stresses are the key to preserve the coordinate objectivity in the Savage-Hutter model. The effect of the anisotropic stress is illustrated by two examples: an axisymmetric dam break and a finite mass sliding on an inclined plane chute. It is found that the propagation of the flow fronts significantly depends on the orientation of the principal axes of the tangential stresses.

Keywords

76A0582B4086-0897M10Gas-kinetic schemeBGK equationextended Savage-Hutter equation
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 5 , May 2013 , pp. 1432 - 1454
Copyright
Copyright © Global Science Press Limited 2013

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