A spectral/finite‐difference approach for narrow‐channel flow with inertia

Abstract

AbstractA hybrid spectral/finite‐difference scheme is proposed to determine the inertial flow inside narrow channels. The flow field is represented spectrally in the depthwise direction, which together with the Galerkin projection lead to a system of equations that are solved using a variable step finite difference discretization. The method is particularly effective for non‐linear flow, and its validity is here demonstrated for a flow with inertia. The problem is closely related to high‐speed lubrication flow. The validity of the spectral representation is assessed by examining the convergence of the method, and comparing with the fully two‐dimensional finite‐volume solution (FLUENT), and the widely used depth‐averaging method from shallow‐water theory. It is found that a low number of modes are usually sufficient to secure convergence and accuracy. Good agreement is obtained between the low‐order description and the finite‐volume solution at low to moderate modified Reynolds number. The depth‐averaging solution is unable to predict accurately (qualitatively and quantitatively) the high‐inertia flow. The influence of inertia is examined on the flow. Copyright © 2003 John Wiley & Sons, Ltd.