Two-dimensional System of equations and Line-by- line TDMA

Whether the discretized momentum Eqns. (28.3) and (28.4) or the pressure correction Eq. (29.5) the final outcome is a system of algebraic equation given by The current values of the dependent variables are to be evaluated from the known values of the coefficients (a's). The evaluation algorithm will be same for the momentum equations and the pressure correction equation.

Figure 30.1

On a rectangular grid, the dependent variables at one point may be expressed in terms of its neighbors (Fig. 30.1) as

where is equivalent to to to to and to