Numerical Methods and Its Solution - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 201

Fig. 7.23 A backward staggered mesh system for the pressure velocity coupling
to the class of iterative methods, which is embodied in a scheme called SIMPLE
where the acronym stands for Semi-Implicit Method for Pressure-Linkage Equations.
This scheme was developed for practical engineering solutions by Patankar and
Spalding (1972) and has found widespread application in the majority of CFD codes.
In this scheme, a guessed pressure field is used to solve the momentum equations,
thus the u, v velocities are obtained. A pressure correction equation, deduced from
the continuity equation, is then solved to obtain a pressure correction field, which
in turn is used to update the velocity and pressure fields. The equations are solved
sequentially which means that an unknown variable is solved one at a time using the
known values of the other variables, and hence only one variable changes at a time.
The guessed fields are iterated where the momentum and continuity equations are
continuously changing to ensure mass conservation.
Variable arrangement on the grid Before describing the SIMPLE scheme, we
present the staggered grid arrangement. The aim of having a staggered grid arrange-
ment for CFD computations is to evaluate the velocity components at the control
volume faces while the rest of the variables governing the flow-field, such as the
pressure, temperature and turbulent quantities, are stored at the central node of the
control volumes. A typical arrangement is depicted in Fig. 7.23 on a structured finite