Equations with Second Derivatives
In lecture 15, the finite volume method was applied to Eqn. (15.1), in which only first derivatives appeared, and produced a relatively straightforward discretization formula given by Eqn. (15.8). The finite volume method requires some modification, when the second derivatives are present in the governing equation.
Let us consider Laplace 's equation
Figure 16.1: Finite Volume for a Curvilinear Grid.
The finite volume method follows the application of the subdomain method to Eqn. (16.1). For the finite volume ABCD as shown in Fig. 16.1, one can write the area integral of (16.1) as
 H.n  |
(16.2) |
where Green's theorem has again been used and now
H. n  |
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