Owing to a very large number of calculations performed, we discuss the results exclusively in terms of the maximum absolute value the spurious velocity (called peak error velocity) generated by the pressure gradient errors. Figure 4 shows the time evolution of the peak error velocity for the first 20 days of integration with the ordinary and compact schemes. The peak error velocity fluctuates rapidly during the first few days integration. After the 5 days of integration, the peak error velocity show the decaying inertial oscillation superimposed into asymptotic values. For the fourth order difference (Figure 4a) the asymptotic value is around 0.19 cm/s for the ordinary scheme and 0.15 cm/s for the compact scheme. For the sixth order difference (Figure 4b) the asymptotic value is near 0.04 cm/s for the ordinary scheme and 0.02 cm/s for the compact scheme.
The steadily approach of the peak error velocities to these values for the three schemes indicates the stability of the computation. Furthermore, the error reduces drastically (22% error reduction for the fourth-order and 50% for the sixth-order) when the compact scheme is used.