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Figure 12.1.
The virtual water column and pipe connections between each of them.
12.1.1 Theory
The concept presented in this article is based on a Web chat by Yann Lombard(Lombard),
which references a paper entitled "Dynamic Simulation of Splashing Fluids" by James F.
O'Brien and Jessica K. Hodgins (O'Brien, 1995). The paper outlines a method of simulat-
ing water interactions based on "columns" of water that are connected together by pipes.
The columns are organized in a regular grid arrangement, and each column is connected
to its immediate neighbors by a virtual pipe. One pipe is used in each of the eight direc-
tions outward from each column: up, down, right, left, upper left, upper right, lower right,
and lower left. The algorithm is used to approximate the amount of fluid that would be
transferred through each of the pipes over a given fixed time step, based on the delta in
height values between each column. This water transfer is then used to modify the virtual
volumes contained in the columns. This then modifies the height values in each column
once again, to be used in the next simulation step. The setup of the columns and pipes is
shown in Figure 12.1.
Using this model lets us provide physical parameters for both the fluid being simu-
lated and the physical characteristics of the columns and grids. Each water column is rep-
resented as a column with a provided constant cross-sectional area. By using a constant
cross-sectional area, we ensure that the volume of fluid contained within the column is
directly proportional to the height of the water in the column, as shown in Equation (12.1):
(12.1)
Once the height of the fluid column is available, we can determine the maximum
pressure within the column based on gravity, the density of the fluid, and the atmospheric
pressure above the column. The greatest pressure in the column will occur at the bottom
of the column, which is where we will assume the pipes are connected at. This maximum
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