Conservation laws in curvilinear coordinates: A short proof of Vinokur’s Theorem using differential forms

摘要

In computational fluid dynamics it is important to maintain strong conservation form in the equations of motion regardless of the coordinate system used. Vinokur’s Theorem says that conservation form can always be maintained. However, the proof is long and has non-obvious steps. In this note a short proof of Vinokur’s Theorem is given which is both simple and illuminating. It uses the theory of differential forms which may also be useful in other algorithmic constructions.