On the parameters of absorbing layers for shallow water models
On the parameters of absorbing layers for shallow water models
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DOI：
10.1007/s10236-009-0243-0
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发表时间：
2010-02
期刊：
影响因子：
2.3
通讯作者：
A. Modave;É. Deleersnijder;É. Delhez
中科院分区：
文献类型：
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作者：
A. Modave;É. Deleersnijder;É. Delhez
吸收/海绵层用作海洋/海洋模型的边界条件进行检查的背景下，浅水方程的目的是尽量减少反射的传出波在计算域的边界。在连续模型中，吸收系数的优化不是问题，因为通过增加吸收系数，可以使出射波的反射系数尽可能小。因此，吸收层的参数的优化是一个纯离散的问题。必须在有效衰减传出波和有限的空间分辨率之间找到平衡，由此产生的空间梯度必须加以描述。使用一维模型作为测试用例，不同的空间分布的吸收系数的性能进行了比较。从纯传播和纯平流问题的理论考虑出发，推导出了吸收系数的两个位移双曲线分布。这些分布表现出良好的性能。它们的自由参数有明确的解释，因此可以在物理基础上确定。使用经典的二维问题的崩溃的一个高斯形的水丘和它的平流的平均电流的两个移位双曲线的属性说明。当考虑完全非线性动力学时，所得边界格式仍具有良好的性能。
Absorbing/sponge layers used as boundary conditions for ocean/marine models are examined in the context of the shallow water equations with the aim to minimize the reflection of outgoing waves at the boundary of the computational domain. The optimization of the absorption coefficient is not an issue in continuous models, for the reflection coefficient of outgoing waves can then be made as small as we please by increasing the absorption coefficient. The optimization of the parameters of absorbing layers is therefore a purely discrete problem. A balance must be found between the efficient damping of outgoing waves and the limited spatial resolution with which the resulting spatial gradients must be described. Using a one-dimensional model as a test case, the performances of various spatial distributions of the absorption coefficient are compared. Two shifted hyperbolic distributions of the absorption coefficient are derived from theoretical considerations for a pure propagative and a pure advective problems. These distribution show good performances. Their free parameter has a well-defined interpretation and can therefore be determined on a physical basis. The properties of the two shifted hyperbolas are illustrated using the classical two-dimensional problems of the collapse of a Gaussian-shaped mound of water and of its advection by a mean current. The good behavior of the resulting boundary scheme remains when a full non-linear dynamics is taken into account.