平流傳輸方程的計算：交錯網格之有限差分法

Computational Tests of Advection Equation: Finite Difference on a Staggered Grid

郭鴻基(Hung-Chi Kuo) ； 柳再明(Tsai-Ming Liu) ； 周仲島(Ben Jong-Dao Jou)

《大氣科學》 18卷2期 (1990/06) Pp. 159-169

摘要

在環境科學裡現存有許多問題，以平流方程形式的傳送問題是非常重要的。找尋合適的數值方法，來計算平流傳送，是不可避免的問題。在本文中，我們使用一維平流傳送方程式探討在交錯網格上的平流傳送問題。文中說明在使用Arakawa C網格時，定義通量所應注意的地方。同時指出通量定義不適當，四階中差分法的精確度將降低。最後並提供和四階定義法一致的通量定義。為了避免因計算而產生不合物理的負值，我們也描述了一至三階的正定義法。

關鍵字

正定義法 ； 差分法 ； 平流方程 ； 交錯網格

並列摘要

There are many problems in atmospheric science where a central concern is the manner in which scalars (e.g. trace constituent, potential vorticity and water vapor) is transported by moving fluid. It is important to find a suitable finite difference algorithm on a staggered grid for this problem. In this paper, we use a simple one-dimensional linear advection equation to study the advective process on the staggered grid. It is illustrated that caution must be taken in defining flux on the staggered C-grid. It is shown that accuracy can be lost in the fourth-order centered differencing in flux is defined improperly. A consistent way of defining flux with the fourth-order finite differencing is presented. To avoid the appearance of negative value, positive definite schemes are also tested.

並列關鍵字

positive definite scheme ； finite difference ； advection equation ； staggered grid