On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation

It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme.