Let us consider inviscid Burger's equation ((9.11)).

This time we let vorticity, which means

(10.1)

The finite difference analog is given by FTCS method as

(10.2)

Let us consider a region running from to see (Figure10.1).

Figure 10.1: Domain running from to .

We evaluate the integral as

(10.3)

Summation of the right hand side finally gives

(10.4)

Eq. (10.4) state that the rate of accumulation of in is identically equal to the net advective flux rate across the boundary of running from to .

Thus the FDE analog to inviscid part of the integral Eq. (10.2) has preserved the conservative property. As such, conservative property depends on the from of the continuum equation used.