The finite difference continuity equation of Leonhard Euler
type: Item
instance of: scholarly article
zbMATH Open document ID: 1350.76004
author: V. M. Ovsyannikov
publication date: 2013-08-13T00:00:00Z
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76N15
Mathematics Subject Classification ID: 76Q05
Mathematics Subject Classification ID: 76-02
zbMATH DE Number: 6198078
zbMATH Keywords: Lagrangian variables
zbMATH Keywords: control volume
zbMATH Keywords: flow instability
zbMATH Keywords: acoustic equation
MaRDI profile type: Publication
title: The finite difference continuity equation of Leonhard Euler
review text: 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.
reviewed by: Oleg Titow
description: scientific article; zbMATH DE number 6198078