Numerical Schemes Comparison in Solving the Problem of Laminar Flow in the Suddenly Expanding Channel

Abstract

The paper studies fluid flow in a two-dimensional channel with sudden expansion (x/h = 2). Calculations were made for the laminar flow mode based on numerical integration of the nonstationary Navier --- Stokes equations. Various flow characteristics were determined at Re = 100--800. Results were obtained for the longitudinal speed profiles in various channel sections and lengths of the primary and secondary vortices at various values of the Reynolds number after the step. The friction coefficient distribution on the channel lower side along its length is presented for various values of the Reynolds number. For the difference approximation of the initial equations, the control volume method was applied; relationship between speed and pressure was found using the SIMPLE procedure. For numerical solution of the problem, the following QUICK schemes were introduced: McCormack's second-order accuracy, Warming --- Cutler --- Lomax's third-order accuracy and Abarbanel --- Gotlieb --- Turkel's fourth-order accuracy. To confirm correctness, numerical results were compared with the experimental data taken from the literature sources