The Effects of the Asselin Time Filter on Numerical Solutions to the Linearized Shallow-Water Wave Equations
The Effects of the Asselin Time Filter on Numerical Solutions to the Linearized Shallow-Water Wave Equations
复制标题
Asselin时间滤波器对线性化浅水波浪方程数值解的影响
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
L. Uccellini
中科院分区：
文献类型：
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作者：
R. Schlesinger;Donald R. Johnson;L. Uccellini
本文用一维无旋转浅水波方程的线性分析方法，研究了Asselin（1972）提出的时间滤波器对蛙跳平流格式和Dufort-Frankel、“laged”和Crank-Nicholson三种扩散格式的稳定性和相位误差的影响。分析认为传播和扩散都单独和组合在一个统一的离散网格上的所有可分辨的波长。主要目的是建立滤波强度参数ν的合适范围，用于抑制计算波模式而不实质上改变物理波模式。在没有传播的情况下，“滞后”格式具有最精确的阻尼物理模式。严重的过阻尼在中间波长呈现滞后计划不如其他两个传播时，和Dufort-Frankel是更可取的Crank-Nicholson，因为更小的计算需求。无论有无滤波，空间截断误差的。
Abstract A one-dimensional linear analysis of the shallow-water wave equations without rotation is used to evaluate the effects of a time filter developed by Asselin (1972) on both stability and phase error of the leapfrog advection scheme and each of three diffusion schemes: Dufort-Frankel, “lagged” and Crank-Nicholson. The analysis considers propagation and diffusion both separately and in combination over all resolvable wavelengths on a uniform discrete grid. The main objective is to establish a suitable range of the filtering intensity parameter ν for suppressing the computational wave mode without materially altering the physical wave mode. Without propagation, the “lagged” scheme has the most accurately damped physical mode. Serious overdamping at intermediate wavelengths renders the lagged scheme inferior to the other two when propagation is present, and Dufort-Frankel is preferable to Crank-Nicholson because of much smaller computing demands. With or without filtering, the space truncation error o...