Commun. Comput. Phys., 13 (2013), pp. 1432-1454. |
Gas Kinetic Scheme for Anisotropic Savage-Hutter Model Wen-Chi Chen ^{1}, Chih-Yu Kuo ^{1*}, Keh-Ming Shyue ^{2}, Yih-Chin Tai ^{3} 1 Division of Mechanics, Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan.2 Department of Mathematics, National Taiwan University, Taipei 106, Taiwan. 3 Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan. Received 19 January 2012; Accepted (in revised version) 25 May 2012 Available online 8 October 2012 doi:10.4208/cicp.190112.250512a 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 non-equilibrium 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. AMS subject classifications: 76A05, 82B40, 86-08, 97M10Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164 Key words: Gas-kinetic scheme, BGK equation, extended Savage-Hutter equation. *Corresponding author. Email: olivech@gate.sinica.edu.tw (W.-C. Chen), cykuo06@gate.sinica.edu.tw (C.-Y. Kuo), shyue@math.ntu.edu.tw (K.-M. Shyue), yctai@mail.ncku.edu.tw (Y.-C. Tai) |