Let us refer to Fig. 1.2.

The grid points are identified by an index which increases in the positive - direction, and an index which increases in the positive -direction. If is the index of point in Fig.1.2, then the point immediately to the right is designated as and the point immediately to the left is and the point directly below is

The basic philosophy of finite difference method is to replace the derivatives of the governing equations with algebraic difference quotients. This will result in a system of algebraic equations which can be solved for the dependent variables at the discrete grid points in the flow field.

In the next lecture we'll look at some of the common algebraic difference quotients in order to be acquainted with the methods related to discretization of the partial differential equations.

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