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ADAPTATION OF AN UPWIND CONSERVATIVE FINITE-VOLUME SCHEME TO DEPTH AVERAGED TURBIDITY CURRENT EQUATIONS

机译:适应逆风保守有限体积方案到深度平均浊度电流方程

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Two explicit numerical schemes to solve depth-averaged equations describing the evolution of a turbidity current over a slope change with a confined condition in the downstream end are proposed and compared. The first scheme corresponds to an adaptation of a recently developed upwind conservative finite-volume scheme, originally intended for solving Saint-Venant equations. The second one is a classical predictorcorrector finite-difference MacCormak scheme. Comparison between the numerical schemes is made based on their physical behavior and, at the same time, contrasting the predicted values for depth-averaged quantities with experimental measurements reported by Garcia (1993). It is concluded that the upwind scheme shows better conservation of quantities and similar precision of results than MacCormak scheme and does not require any special treatment, such as the artificial viscosity used in the latter, thus being more efficient in computational sense. The proposed scheme has the ability to capture fronts and hydraulic jumps in a variety of hydrodynamic situations, however it may present some stability problems in the case of reversal flows.
机译:提出了两个明确的数字方案,用于解决描述浊度电流在斜坡变化中的浊度电流的演变的深度平均方案,并进行了比较了下游端的限制条件。第一方案对应于最初开发的Unumnind保守有限体积方案的适应,最初用于求解圣文鸣方程。第二个是一种经典预测粗磁体有限差异的MacCormak方案。数值方案之间的比较是基于其物理行为进行的,并且同时对比具有Garcia(1993)报告的实验测量的深度平均量的预测值。结论是,UPUNNIND方案表明,比MacCormak方案更好地保护数量和类似的效果,并且不需要任何特殊处理,例如后者中使用的人工粘度,从而在计算意义上更有效。所提出的方案具有在各种流体动力学情况下捕获前端和液压跳跃的能力,但是在逆转流动的情况下可能存在一些稳定性问题。

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