Numerical Study of Laminar Flow Using Various Difference Schemes
Abstract
Mathematical modeling plays a key role in econometrics as it is a field where statistics and mathematics are used to analyze economic data and develop economic models. This paper presents a numerical study of laminar flow in a suddenly expanding channel using various computational schemes. The Na-vier-Stokes equation was used to numerically solve the laminar flow in the channel. To calculate the Navier-Stokes equation, an explicit scheme of the third order of accuracy QUICK (Quadratic Upstream Interpolation for Con-vective Kinematics) and a second order of accuracy implicit against flow US (Up-wind scheme) schemes were used. For the difference approximation of the initial equa-tions, the finite difference method was applied, and the rela-tionship between velocities and pressure was found using the SIMPLE pro-cedure. The paper presents a two-dimensional geometry of an expansion channel with an expansion ratio of 1:2. Based on this geometry, results were obtained with Reynolds numbers of 100, 400, 600, and 800. Velocity plots at Reynolds numbers of 100 and 400 were compared with experimental re-sults at different sections. Graphs of friction coefficients were obtained for various values of Reynolds numbers. Speed profiles were compared using QUICK and implicit schemes. In addition, longitudinal velocity isolines are present-ed for Reynolds numbers of 100, 400, 600, and 800. It is shown that the re-sults are practically the same for the two presented finite-difference schemes for small Reynolds numbers. At large values of the Reynolds number, the numerical results obtained by the implicit scheme showed better agreement with the experimental results than by the QUICK scheme. And also the pa-per presents the primary and secondary flow vortices as isolines.