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題名 | 高階尤拉正定平流格式的研究= |
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作者 | 黃清勇; 廖建誠; |
期刊 | 大氣科學 |
出版日期 | 19950900、19951200 |
卷期 | 23:3/4 民84.09-12 |
頁次 | 頁287-310 |
分類號 | 328.21 |
語文 | chi |
關鍵詞 | 正定; Bott格式; Positive definiteness; Bott schemes; |
中文摘要 | 本文針對正定(positive definite)物理量平流作用研究其特殊數值方法。文中比較兩種通量形式(flux form)的尤拉格式,一為Bott格式利用多項式插分法,是Bott (1989a, b)所提出,另一為NIC□格式利用三次樣條(cubic spline)插分法,是Emde (1992)所提出,理論上二者皆保證正純量場及嚴格的質量保守。文中包含均勻流場測試、旋轉流場測試、強變形流場測試及循環性純變形流場測試。在平滑流場(均勻流場與旋轉流場),面積保有條件導出的六階Bott格式表現最佳,於六次旋轉測試仍保有短波振幅達82%。對較長波而言,四階的Bott格式比NIC□格式略優,對短波而言二者則在伯仲之間。但是在強變形流場中,所有Bott格式都有輕度的不穩定,而NIC□格式格式則為穩定的。在循環性純變形流場中,測試循環多次後,NIC□格式要比四階及六階Bott格式更能忍受數值耗散。本文所探討的高階正定尤拉通量形式格式,在所有流場測試均嚴格保守正定質量,其綜合表現確屬優異。 |
英文摘要 | Special numerical methods for positive-definite physical advection are investigated in this study. Two advection schemes in flux form, Bott's scheme using Lagrangian polynomial interpolation (Bott, 1989a, b) and NIC□ scheme using cubic spline interpolation (Emde, 1992) are compared, both the oretically maintaining positiveness of scalars and strict mass conservation. This study includes numerical tests of uniform flow, rotational flow, strong deformational flow and cycling pure deformational flow. For smooth flow (uniform flow and rotational flow), the sixth-order area-preserving Bott's scheme performs best among the schemes, retaining 82% of shortwave amplitude. For long waves, fourth-order Bott's schemes are slightly better than NIC□, but they are equally well for shortwaves. However, all Bott's schemes are slightly unstable in the strong deformational flow test and the NIC□ scheme is stable. For cycling pure deformational flow, the NIC□ schemes is more tolerable for numerical dissipation after more cycles. The high-order Eulerian positive-definite advection schemes in flux form do preserve total mass in all the flow tests in this study, and their overall performances are remarkably good. |
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