|
|||||
|
|
Completely Conservative and Oscillationless Semi-Lagrangian Schemes for Advection Transportation |
|
| Authors: | Feng Xiao Takashi Yabe |
| Institution: | Department of Energy Sciences, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, Yokohama, 226-8502, Japanf1;Department of Mechanical Engineering and Science, Tokyo Institute of Technology, 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8552, Japan, f2;b Frontier Research System for Global Change, SEAVANS North, 1-2-1 Shibaura Minato-ku, Tokyo, 105-6791, Japan |
| Abstract: | In this paper, we present a new type of semi-Lagrangian scheme for advection transportation equation. The interpolation function is based on a cubic polynomial and is constructed under the constraints of conservation of cell-integrated average and the slope modification. The cell-integrated average is defined via the spatial integration of the interpolation function over a single grid cell and is advanced using a flux form. Nonoscillatory interpolation is constructed by choosing proper approximation to the cell-center values of the first derivative of the interpolation function, which appears to be a free parameter in the present formulation. The resulting scheme is exactly conservative regarding the cell average of the advected quantity and does not produce any spurious oscillation. Oscillationless solutions to linear transportation problems were obtained. Incorporated with an entropy-enforcing numerical flux, the presented schemes can accurately compute shocks and sonic rarefaction waves when applied to nonlinear problems. |
| Keywords: | Abbreviations: atmospheric modelingAbbreviations: computational algorithmAbbreviations: semi-Lagrangian schemeAbbreviations: linear and nonlinear transportation equationsAbbreviations: mass conservationAbbreviations: shock wave |
| 本文献已被 ScienceDirect 等数据库收录！ | |