High‐order essentially local extremum diminishing schemes for environmental flows

Abstract

AbstractThe accuracy of numerical simulation is greatly affected by the applied convective schemes for high Reynolds number environmental flows. The convection for any scalar equation should theoretically be a purely transport process. Simple monotonic convective schemes produce smooth and stable solutions. However, the results are not reliable and possibly introduce excessive artificial diffusion (AD). We develop a new high‐order monotonic formulation of essentially local extremum diminishing (ELED) schemes, using a simple algorithm to minimize the AD introduced by the convective schemes. The high‐order scheme is based on the Quadratic Upstream Interpolation for Convective Kinematics formula in order to compare the results with Simple High‐Accuracy Resolution Program. The resulting algorithm is applied to a two‐dimensional standing interfacial wave problem and extended to three‐dimensional turbulent coastal upwelling flows using large eddy simulation (LES). These examples allow sharp density interfaces in the domain, which may cause severe dispersion errors when high‐order schemes are used, whereas most monotonic schemes produce significant AD. When a finer grid is used, the AD based on the Jameson, Schmidt and Turkel formula (Int. J. Comput. Fluid Dyn. 1995; 4:171–218) drops dramatically. The new high‐order ELED schemes exhibit comparable accuracy to other high‐order monotonic schemes and introduce less diffusion in the unsteady environmental flow simulations. The current results of LES show that the energy transfer inherent in the monotonic convection schemes may contribute non‐negligibly to the turbulence. It is found that a dynamic‐mixed model is able to compensate the effect of the convection schemes and provides correct flow behaviors in reality. Copyright © 2008 John Wiley & Sons, Ltd.