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首页> 外文期刊>Bulletin of the American Physical Society >APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Consistent three-equation model for thin films.
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APS -70th Annual Meeting of the APS Division of Fluid Dynamics- Event - Consistent three-equation model for thin films.

机译：APS-流体动力学APS分部第70届年会-事件-一致的薄膜三方程模型。

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Numerical simulations of thin films of newtonian fluids down an inclined plane use reduced models for computational cost reasons. These models are usually derived by averaging over the fluid depth the physical equations of fluid mechanics with an asymptotic method in the long-wave limit. Two-equation models are based on the mass conservation equation and either on the momentum balance equation or on the work-energy theorem. We show that there is no two-equation model that is both consistent and theoretically coherent and that a third variable and a three-equation model are required to solve all theoretical contradictions. The linear and nonlinear properties of two and three-equation models are tested on various practical problems. We present a new consistent three-equation model with a simple mathematical structure which allows an easy and reliable numerical resolution. The numerical calculations agree fairly well with experimental measurements or with direct numerical resolutions for neutral stability curves, speed of kinematic waves and of solitary waves and depth profiles of wavy films. The model can also predict the flow reversal at the first capillary trough ahead of the main wave hump.
机译：由于计算成本的原因，在倾斜平面上的牛顿流体薄膜的数值模拟使用简化的模型。这些模型通常是通过在流体深度上用长波极限中的渐近方法对流体力学的物理方程求平均值而得出的。二方程模型基于质量守恒方程，动量平衡方程或功-能量定理。我们表明，不存在既一致又理论上连贯的两方程模型，并且需要第三个变量和三方程模型来解决所有理论矛盾。在各种实际问题上测试了两个方程组和三个方程组的线性和非线性性质。我们提出了一种新的一致的三方程模型，该模型具有简单的数学结构，可以实现简单而可靠的数值分辨率。数值计算与实验测量结果非常吻合，或者与中性稳定性曲线，运动波和孤立波的速度以及波浪膜的深度剖面的直接数值分辨率非常吻合。该模型还可以预测主波峰之前的第一个毛细波谷的逆流。

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