Design and experiments of a new positive-definite renormalization scheme for advection-diffusion differential equation

Hao Shi-Feng; Cui Xiao-Peng

doi:10.7498/aps.61.039204

Abstract

Total mass conservation is a basic property of advection-diffusion differential equation. While since the difference schemes is not positive-definite, total mass is not conserved, caused by negative mass in numerical integration. Aiming at this problem, a new positive-definite renormalization scheme is proposed based on the physical meaning of negative mass. Experiments of point-source advection-diffusion show that the new renormalization scheme not only solves the positive-definite problem of advection-diffusion differential equation, but also keeps the property of total mass conservation. Compared with the renormalization scheme in the WRF model, the new positive-definite renormalization scheme has virtues of clear physical meaning and easier mannpulation.

Keywords:

Authors and contacts

Hao Shi-Feng¹,
Cui Xiao-Peng²

1.
Zhejiang Meteorology Observatory, Hangzhou 310017, China;
2.
LACS, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
Funds: Project supported by the National Basic Research Program of China (Grant No. 2009CB421505), Open Project of Zhejiang Meteorological Bureau, China (Grant No. kf2007007), the Social Development Program of Department of Science and Technology in Zhejiang, China (Grant No. 2008C23012), and the National Natural Science Foundation of China-Regional Cooperation Project (Grant No. 40921160379).

References

[1]	Xu D H, Zhu R 2000 Quart. J. Appl. Meteorol. 11 1 (in Chinese) [徐大海, 朱蓉 2000 应用气象学报 11 1]
[2]	Bott A 1989 Mon. Wea. Rev. 117 1006
[3]	Smolarkiewicz P K 1989 Mon. Wea. Rev. 117 2626
[4]	Skamarock W C 2006 Mon. Wea. Rev. 134 2241
[5]	Skamarock W C 2009 Mon. Wea. Rev. 137 488
[6]	Huang S X, Cai Q F, Xiang J 2007 Acta Phys. Sin. 56 3022 (in Chinese) [黄思训, 蔡其发, 项杰 2007 物理学报 56 3022]
[7]	Zhou Y, Hou Z M, Liu Y D 2003 Numerical Weather PredictionBasis (Beijing: China Meteorological Press) p124 (in Chinese) [周毅, 候志明, 刘宇迪 2003 数值天气预报基础 (北京: 气象出版社) 第127页]

Cited By

[1]	Xu D H, Zhu R 2000 Quart. J. Appl. Meteorol. 11 1 (in Chinese) [徐大海, 朱蓉 2000 应用气象学报 11 1]
[2]	Bott A 1989 Mon. Wea. Rev. 117 1006
[3]	Smolarkiewicz P K 1989 Mon. Wea. Rev. 117 2626
[4]	Skamarock W C 2006 Mon. Wea. Rev. 134 2241
[5]	Skamarock W C 2009 Mon. Wea. Rev. 137 488
[6]	Huang S X, Cai Q F, Xiang J 2007 Acta Phys. Sin. 56 3022 (in Chinese) [黄思训, 蔡其发, 项杰 2007 物理学报 56 3022]
[7]	Zhou Y, Hou Z M, Liu Y D 2003 Numerical Weather PredictionBasis (Beijing: China Meteorological Press) p124 (in Chinese) [周毅, 候志明, 刘宇迪 2003 数值天气预报基础 (北京: 气象出版社) 第127页]

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