Abstract The collapse of a submerged granular pile under the action of the gravity force is investigated by means of a depth averaged model (hereinafter DAM). The granular pile is a mixture of solid particles and ambient liquid, totally covered by a layer of ambient liquid. The DAM is obtained by depth-averaging the mass and momentum equations of the mixture and the ambient fluid and is aimed at providing estimates of technical quantities regarding the considered phenomenon. The DAM is numerically solved by adopting an equivalent Discrete Boltzmann Equation model (hereinafter DBE) as solution method. The main advantage yielded by the DBE is the possibility to turn the original system of strongly non linear partial differential equations, which would require the resort to complex numerical schemes, into a purely advective, linear, first order one. Previously published experimental and numerical data, relative to the collapse of loose rectangular granular piles in water, are reproduced by the proposed model and a satisfactory agreement is found, revealing that the DAM is able to describe reliably the overall dynamics, in terms of quantities of technical interest as the height of the submerged granular flow and the instantaneous position of its front.

中文翻译：

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松散矩形颗粒桩在水中倒塌的深度平均建模

摘要 利用深度平均模型（DAM）研究了沉水颗粒桩在重力作用下的倒塌问题。颗粒堆是固体颗粒和环境液体的混合物，完全被一层环境液体覆盖。DAM 是通过对混合物和环境流体的质量和动量方程进行深度平均而获得的，旨在提供有关所考虑现象的技术量的估计。DAM采用等效的离散玻尔兹曼方程模型（以下简称DBE）作为求解方法进行数值求解。DBE 产生的主要优点是可以将强非线性偏微分方程的原始系统（这将需要求助于复杂的数值方案）转变为纯平流、线性、一阶方程。