A. Abd Manaf et al. (Eds.): ICIEIS 2011, Part III, CCIS 253, pp. 82–94, 2011.
© Springer-Verlag Berlin Heidelberg 2011
Staggered Grid Computation of Fluid Flow
with an Improved Discretisation of Finite Differencing
Nursalasawati Rusli
1,2
, Ahmad Beng Hong Kueh
2
, and Erwan Hafizi Kasiman
2
1
Institute of Engineering Mathematics, Universiti Malaysia Perlis,
02000 Kuala Perlis, Perlis, Malaysia
2
Steel Technology Centre, Faculty of Civil Engineering,
Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia
nursalasawati@unimap.edu.my, {kbhahmad,erwanhafizi}@utm.my
Abstract. The present paper models the fundamental problems of fluid flow
using a discretely improved finite difference method on a staggered
computational grid. The developed finite difference formulation is applied to
well-established benchmark problems, namely, the lid-driven cavity flow, the
developing laminar flow in a straight rectangular duct and the backward-facing
step flow. Excellent agreements have been found for all cases. Also, this
approach has successfully handled the pressure of the flow that has been long
considered as one of the main problems in using the finite difference method.
Keywords: finite difference method, Navier-Stokes equations, incompressible
flow, staggered grid.
1 Introduction
Over the past few decades, numerical modelling of fluid flow has been a major topic
of research in modern science and engineering [1]. Computational fluid dynamics
(CFD) occupies one of the key physical disciplines that involve the description of
fluid flow in terms of mathematical models which comprise convective and diffusive
transports of matters. Basically, it constitutes the groundwork covering the fields of
mechanical engineering, marine engineering, aeronautics and astronautics, civil
engineering and bioengineering, to name a few. Inherent in the core of fluid flow
study are the mathematical models that consist of a set of governing equations in the
form of ordinary or partial differential equations. Although a great account of
analytical solutions for CFD is available, in practical applications, it is customary to
resolve the solutions in numerical form. One of the chief techniques frequently used
in the investigation of CFD is the finite difference method (FDM).
In obtaining solutions for CFD problems, one of the main concerns of the FDM is
the handling of the pressure of the flow. In general, physical specification of pressure is
absent, as it is implicitly correlated to the problem description. Even though there are
three equations for the three unknowns u, v, p, there is no explicit equation which can
be used for pressure. In most finite difference solution schemes for incompressible
steady flows, the pressure field is obtained from a Poisson equation which is derived