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18 June 2018 Analytical and Explicit Solutions to Implicit Wave Friction-Factor Equations Based on the Lambert W Function
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Abstract
Li, S. and Liu, Y., 2018. Analytical and explicit solutions to implicit wave friction-factor equations based on the Lambert W function.Calculation of the friction factor of turbulent oscillatory fluid flow is a significant issue in accessing bed shear stress and sediment entrainment in coastal areas. A fast, robust calculation is necessary for intensive scientific simulations. However, some widely used friction-factor equations belong to the group of implicit and transcendental equations. Common procedures for obtaining accurate solutions are based on root-solving techniques such as the Newton–Raphson iterative method, with substantial computation cost and potential failure of solution convergence. The present note offers a simple and highly accurate procedure for explicitly calculating the friction factors. First, explicit analytical solutions of the friction-factor equations are derived using the Lambert W function, which is a newly recognized elementary transcendental function. Then, the analytical solutions are numerically calculated by simply calling the fast algorithms of the Lambert W function that is available in the libraries of many kinds of software of widely applied numerical computing environments. For practical purposes, this note also compares several fast algorithms of the function.
©Coastal Education and Research Foundation, Inc. 2018
Shaowu Li and Ye Liu "Analytical and Explicit Solutions to Implicit Wave Friction-Factor Equations Based on the Lambert W Function," Journal of Coastal Research (JCR) 34(6), (18 June 2018). https://doi.org/10.2112/JCOASTRES-D-17-00181.1
Received: 17 October 2017; Accepted: 10 April 2018; Published: 18 June 2018
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