Applications of the artificial compressibility method for turbulent open channel flows

Abstract

<jats:title>Abstract</jats:title><jats:p>A three‐dimensional (3‐D) numerical method for solving the Navier–Stokes equations with a standard <jats:italic>k–ε</jats:italic> turbulence model is presented. In order to couple pressure with velocity directly, the pressure is divided into hydrostatic and hydrodynamic parts and the artificial compressibility method (ACM) is employed for the hydrodynamic pressure. By introducing a pseudo‐time derivative of the hydrodynamic pressure into the continuity equation, the incompressible Navier–Stokes equations are changed from elliptic‐parabolic to hyperbolic‐parabolic equations. In this paper, a third‐order monotone upstream‐centred scheme for conservation laws (MUSCL) method is used for the hyperbolic equations. A system of discrete equations is solved implicitly using the lower–upper symmetric Gauss–Seidel (LU‐SGS) method. This newly developed numerical method is validated against experimental data with good agreement. Copyright © 2005 John Wiley &amp; Sons, Ltd.</jats:p>