Assessment of the IVA3 code for multifield flow simulation. Formal report Page: 41 of 71
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Revision of the IVA3 strategy may prove, upon further study, to be ad-
visable. First, however, we present the finite difference equations in present
use, based on the strategy just indicated.
3.2 IVA3 differencing scheme
3.2.1 Staggered grid and index convention
The discretization of the multifield flow equations is based on the staggered
grid which is commonly used for fluid dynamics. The computational region is
divided into an orthogonal grid of cells. The balances of mass and entropy are
written for each cell. Each dependent variable has a principal site for each
cell. Material properties of the fields, such as al, pt, se, and the pressure
P have their principal sites at the center of each cell. The cells may thus
be referred to as material cells. Velocities have their principal sites at the
centers of the cell faces, with each velocity component situated on the cell
face to which it is normal.
Three indices i, j, k identify each cell in the grid, specifically the cell
center. That is, the index triple (i, j, k) identify the principal site of the
material property variables. The principal sites of the velocity components
are therefore (i + 1/2, j, k) for ul; (i, j + 1/2, k) for vi; and (i, j, k + 1/2) for
w1. These principal sites turn out to be very convenient for writing the finite
difference form of the balance equations. However, in several instances, a
variable will appear in the finite difference equations at a location other than
its principal site, and when this happens, the variable will be expressed in
terms of the neighboring principal site values by interpolation.
In order to maintain some readability of the discretized equations, a sub-
script convention will be used. Any variable taken at its principal site will be
written with all indices suppressed. Only when secondary sites appear will
indices be written explicitly, and then only those indices differing from the
principal site values need be shown. (Occasionally for emphasis a principal
site index may be written explicitly.) Thus36
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Stewart, H. B. Assessment of the IVA3 code for multifield flow simulation. Formal report, report, July 1, 1995; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc793212/m1/41/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.