Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations
Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations
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DOI：
10.1063/1.1426103
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发表时间：
2002-01-01
影响因子：
4.6
通讯作者：
Manneville, P
中科院分区：
文献类型：
--
作者：
Ruyer-Quil, C;Manneville, P
我们研究了我们[Ruyer-Quil and Manneville， Eur]得到的沿斜面向下的膜流二维模型的可靠性。理论物理。[j] .光子学报，2004,(3):444 - 444。这样的模型通常涉及薄膜的局部厚度h，局部流速q，以及可能的其他局部厚度平均值，从而消除了横向流自由度。在线性阶段，波包的预测性质与Brevdo的精确结果非常吻合[J]。流体力学，1999,37(1999)]。与Liu [Phys]的实验室实验比较，也令人满意地恢复了波的非线性发展。数值模拟[J] .中国科学：地球科学，2014(5)。流体力学，325,163(1996)]。在基于速度场多项式展开的建模策略中，在长波长展开中存在给定阶数的最优模型。随着加权残差逼近阶数的增加，研究了逼近最优的收敛性。我们的模型准确、经济地预测了相对较高雷诺数下膜流的线性和非线性特性，从而提供了有价值的理论和应用研究前景。(C) 2002年美国物理研究所。
We study the reliability of two-dimensional models of film flows down inclined planes obtained by us [Ruyer-Quil and Manneville, Eur. Phys. J. B 15, 357 (2000)] using weighted-residual methods combined with a standard long-wavelength expansion. Such models typically involve the local thickness h of the film, the local flow rate q, and possibly other local quantities averaged over the thickness, thus eliminating the cross-stream degrees of freedom. At the linear stage, the predicted properties of the wave packets are in excellent agreement with exact results obtained by Brevdo [J. Fluid Mech. 396, 37 (1999)]. The nonlinear development of waves is also satisfactorily recovered as evidenced by comparisons with laboratory experiments by Liu [Phys. Fluids 7, 55 (1995)] and with numerical simulations by Ramaswamy [J. Fluid Mech. 325, 163 (1996)]. Within the modeling strategy based on a polynomial expansion of the velocity field, optimal models have been shown to exist at a given order in the long-wavelength expansion. Convergence towards the optimum is studied as the order of the weighted-residual approximation is increased. Our models accurately and economically predict linear and nonlinear properties of film flows up to relatively high Reynolds numbers, thus offering valuable theoretical and applied study perspectives. (C) 2002 American Institute of Physics.