Divergence Form for Bed Slope Source Term in Shallow Water Equations
Divergence Form for Bed Slope Source Term in Shallow Water Equations
复制标题
DOI：
10.1061/(asce)0733-9429(2006)132:7(652
复制
发表时间：
2006-07
影响因子：
2.4
通讯作者：
A. Valiani;L. Begnudelli
中科院分区：
文献类型：
--
作者：
A. Valiani;L. Begnudelli
本文提出了一种新的浅水方程数值解中床坡源项的处理方法。所提出的方法包括写的床坡源项作为一个适当的矩阵的发散，与静力由于底部坡度。这种技术是建立在分析推理和物理基础上的，因此它可以很容易地应用于广泛的数值模型，因为它完全独立于任何采用的离散化技术，并需要最小的计算工作量。在这里，我们展示了一个应用程序的Godunov型模型，二阶精确的空间和时间，基于有限体积法。所提出的技术导致一个强大的改进，在源项的数值处理，特别是对于稳态，其中通量梯度是完全平衡的源项。相对于不同的现有方法，保持了令人惊讶的简单程度。数值模型已被应用到一组经典的测试案例和选定的实验室实验，以验证其稳定性，准确性和适用性，以实际的现实世界的情况下。
A novel technique is presented for the treatment of the bed slope source terms within the numerical solution of the shallow water equations. The proposed method consists of writing the bed slope source term as the divergence of a proper matrix, related to the static force due to bottom slope. Such a technique is founded on analytical reasoning and is physically based, so that it can be easily applied to a wide range of numerical models, as it is completely independent of any adopted discretization technique, and requires a minimum computational effort. Herein, we show an application to a Godunov-type model, second order accurate both in space and time, based on the finite-volume method. The presented technique leads to a strong improvement in the source terms numerical treatment, especially for steady states, in which flux gradients are exactly balanced by source terms. A surprising degree of simplicity is maintained, with respect to different existing methods. The numerical model has been applied to a set of classical test cases and to a selected laboratory experiment, in order to verify its stability, accuracy, and applicability to practical real-world cases.