8.14.1 The Effect of Numerical Roundoff on Pressure Calculation in Low-Mach-Number Flow

In low-Mach-number compressible flow, the overall pressure drop is small compared to the absolute static pressure, and can be significantly affected by numerical roundoff. To understand why this is true, consider a compressible flow with ${\rm M} << 1$. The pressure changes, $\Delta p$, are related to the dynamic head, $\frac{1}{2} \gamma p {\rm M}^2$, where $p$ is the static pressure and $\gamma$ is the ratio of specific heats. This gives the simple relationship $\Delta p/p \sim {\rm M}^2$, so that $\Delta p/p \rightarrow\ 0$ as ${\rm M} \rightarrow\ 0$. Therefore, unless adequate precaution is taken, low-Mach-number flow calculations are very susceptible to roundoff error.