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在大多数数值模式中,为了消除小尺度(波长接近两倍网格距)的波动,必须使用数值耗散或滤波技术。然而,很少有人意识到,常规的耗散或滤波方案自身会引入噪声、例如,大部分滤波器在对梯度变化剧烈或存在陡峭坡度的气象场进行滤波时会遇到困难,即在其结果中不可避免地出现无意义的高频数值振荡(上冲和下冲)、特别是当耗散或滤波应用于有限区域模式时,错误的边值效应往往会严重破坏模式解。 本文分析了常用的耗散或滤波方法的优缺点,提出了一种新型的单调性数位滤波器。它可以防止在物理场出现不连续或者接近不连续时由于计算激波和吉布斯振荡引起的上冲和下冲现象,与此同时仍能保持滤波的高选择特性。此外,新滤波器还采用了隐式计算方案,因而能够轻而易举地解决有限区域模式中的边界退化问题。
In most numerical modes, numerical dissipation or filtering techniques must be used in order to eliminate fluctuations in small scales (wavelengths close to twice the grid spacing). However, few realize that conventional dissipation or filtering schemes introduce noise themselves, for example most filters encounter difficulties in filtering a meteorological field with a steep gradient or a steep grade, It is inevitable that there are insignificant high-frequency numerical oscillations (overshoot and undershoot), especially when the dissipation or filtering is applied to the finite-area mode, erroneous boundary-value effects tend to seriously undermine the mode solution. This paper analyzes the advantages and disadvantages of the commonly used methods of dissipation or filtering, and proposes a new monotonic digital filter. It prevents overshoots and undershoots caused by computational shocks and Gibbs oscillations when the physics field appears discontinuous or nearly discontinuous while still maintaining the high selectivity of filtering. In addition, the new filter also uses an implicit calculation scheme, which can easily solve the problem of boundary degeneration in the finite region mode.