Number：

01100009

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Name：

呂明芳

Titles：

Associate professor

Author：

Ming-Fang Lu, Hsing-Juin Lee and Yu-His Chih

Paper name：

Inherent Numerical Discretization Dilemma Analysis of Euler Equation

Name of activity：

International Journal of Mechanical Engineering Education Vol.37,n3

Keywords：Euler equations, Numerical discretization/CFD, Tracing inherent dilemma, Bernoulli equation factorization.

Abstract：Euler equations derived in 1755 are among the most important equations for general fluid analysis. Although this fundamental governing eqation looks simple at first glancer for incompressible, inviscid fluid flow, it does lead to crucial numerical discretization dilemma related to existence, uniqueness, stability and oscillation problems. Take gradual pipe expansion flow for instance, in the process of deriving Euler equation, the seemingly innocent artificial equalization of crosswise and forward-biased streamwise pressures will give serious discretization error compared with Bernoulli equation, i.e. the wall pressures P_W = P+dP already disappeared from Euler equation will later ghostly bring about troublesome problems, and even violate the fundamental energy principle. Various numerical measures such as artifical viscosity and streamline upwinding are devised awkwardly with the high risk of flow field contamination in an attempt to somehow manipulate some energy dissipation when dealing with incompressible fluid flow. In this research, for the sake of finding the real culprit, we re-scrutinize the original deriving process of Euler equation and insightfully compare the discretized Euler equation with factorized Bernoulli equation, in order to find the inherent ture pathology leading to these serious numerical discretization dilemmas of Euler equation.

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