The finite difference continuity equation of Leonhard Euler (Q2842259)

This work derives thoroughly the finite difference continuity equation for fluid and gas in Lagrangian variables. The derivation takes high time derivatives of the deformation of the control volume into account and is also applied to the acoustic equation. It is shown that, under some conditions, the terms of the modified nonhomogeneous wave eqation are comparable with the traditional ones. This can lead to the formation of physical flow instability in separation regions near the rear part of the body, which was often erroneously attributed to a bad convergence of the numerical method.NEWLINENEWLINE The author gives a detailed historical overview, and concludes the work with abridged English, German and French versions. The monograph will be of great interest to those physicists and mathematicians involved in axiomatical foundations of gas dynamics.