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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.
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Keywords:
- positive-definite /
- renormalization scheme /
- total mass conservation
[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 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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[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 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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