A three-dimensional flow of air is modeled using the MacCormack scheme. The flow velocity is estimated to be between 1 and \(200 \mathrm{~m} / \mathrm{s}\). The computational grid has \(\Delta x=\Delta y=10^{-2} \mathrm{~m}\) and variable step in the \(z\)-direction \(10^{-3} \leq \Delta z \leq 10^{-2} \mathrm{~m}\). Taking the air properties as \(ho=\) \(1.2 \mathrm{~kg} / \mathrm{m}^{3}, \mu=1.81 \times 10^{-5} \mathrm{~kg} / \mathrm{m} \mathrm{s}\), and \(a=340 \mathrm{~m} / \mathrm{s}\) (approximately the properties at \(20^{\circ} \mathrm{C}\) ), find the maximum time step that guarantees numerical stability of solution.