ON A BI-LAYER SHALLOW WATER MODEL WITH RIGID-LID HYPOTHESIS
ON A BI-LAYER SHALLOW WATER MODEL WITH RIGID-LID HYPOTHESIS
复制标题
具有刚性盖假设的双层浅水模型
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. Peybernes
中科院分区：
文献类型：
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作者：
B. D. Martino;P. Orenga;M. Peybernes
在本文中，我们提出了一个新的模式，双层浅水问题使用的刚性盖假设。该模型遵循通常的双层模型，可以大大减少模拟的计算时间。但出现了一些数学和数值上的困难。特别地，我们在方程中观察到1/hi（其中hi是层的厚度）形式的一些项，并且我们不能证明hi > 0。为了避免这个困难，我们用Hi > β > 0代替这些术语中的hi，其中Hi是层的特征厚度。如果hi的波动很小（通常是这种情况），则该假设是现实的。然后，我们证明了这个近似问题的存在性和正则性结果，这表明数值格式的收敛性。接下来，我们提出了一些比较结果，在一个理想的配置之间的模型和经典的双层浅水模式。
In this paper, we present a new model for a bi-layer shallow water problem using the rigid-lid hypothesis. This model follows from the usual bi-layer model and can drastically decrease the computational time of simulation. But some mathematical and numerical difficulties appear. Particularly, we observe in the equations some terms in the form of 1/hi (where hi is the thickness of the layer) and we are not able to prove that hi > 0. To circumvent this difficulty, we replace in these terms hi by Hi > β > 0, where Hi is a characteristic thickness of the layer. This hypothesis is realistic if the fluctuations of hi are small, which is generally the case. Then, we prove existence and regularity results for this approximated problem which shows the convergence of the numerical scheme. Next, we present some comparative results in an idealized configuration between this model and the classical bi-layer shallow water model.