Analytical Solution for Testing Debris Avalanche Numerical Models
Analytical Solution for Testing Debris Avalanche Numerical Models
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DOI：
10.1007/s000240050018
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发表时间：
2000-08
影响因子：
2
通讯作者：
A. Mangeney;P. Heinrich;R. Roche
中科院分区：
文献类型：
--
作者：
A. Mangeney;P. Heinrich;R. Roche
本文给出了斜面上一维溃坝问题的解析解。该解决方案用于测试为碎片雪崩开发的数值模型。我们考虑一个在一个方向上具有无限长度的大坝，其中物质在初始时刻从静止状态释放出来。我们用解析和数值方法求解了在地形链接坐标系中导出的深度平均长波方程。数值解和解析解提供了流动底部的库仑型摩擦定律。该解析解是用特征化方法得到的，它描述了在角大于摩擦角的条件下，沿恒定斜率的流动。数值模型采用基于godunov格式的有限差分方法。解析结果与数值结果的比较表明，数值方法具有显著的稳定性和精度，以及处理强不连续面的能力。
—We present here the analytical solution of a one-dimensional dam-break problem over inclined planes. This solution is used to test a numerical model developed for debris avalanches. We consider a dam with infinite length in one direction where material is released from rest at the initial instant. We solve analytically and numerically the depth-averaged long-wave equations derived in a topography-linked coordinate system. The numerical and analytical solutions provide for a Coulomb-type friction law at the base of the flow. The analytical solution is obtained by using the method of characteristics and describes the flow over a constant slope, provided that the angle is higher than the friction angle. The numerical model utilizes a finite-difference method based on a Godunov-type scheme. Comparison between analytical and numerical results illustrates the remarkable stability and precision of the numerical method as well as its ability to deal with strong discontinuities.