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【媒體報導】興大李興軍破解流體動力學核心公式體系之歷史性嚴重推導錯誤

更新時間:2012-06-29 18:11:34 / 張貼時間:2012-06-28 08:54:26
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興大李興軍破解流體動力學核心公式體系之歷史性嚴重推導錯誤

張貼. 2012/06/28 08:53  祕書室媒體公關組  .

 
 

                                                                                                                              稿源:2012-06-27/中央社

流體動力學對火箭、飛機、船舶、潛艇、汽車等,甚至心臟血流的分析及設計,都是非常重要的學術領域。尤拉方程式於1755年導出之後,一直是流體力學分析中最重要之核心公式。對於不可壓縮、非黏性流而言,此統御公式看似相當優雅簡潔,但在理論分析時卻常遭遇致命的存在與惟一問題,加上近代數值計算時又有嚴重的穩定與振盪問題,多年來一直極度困擾著學界。

國立中興大學機械系李興軍教授帶領的研究團隊,包括江俊顯、遲毓熙、王蜀偉、呂明芳等研究生,最近發表於英國著名的“International Journal of Mechanical Engineering Education”之研究論文“The Life and Death of Euler, Bernoulli, Navier-Stokes Equations and Associated CFD for So-called Incompressible Fluid Flow”〈Vol.39.2〉及“Inherent Numerical Discretization Dilemma Analysis of Euler Equation”〈Vol.39.3〉破解了看似神聖不可侵犯的尤拉、柏努利及相關的N-S流體動力公式體系,在當初就暗藏著彷若無辜但卻致命的推導錯誤!─亦即想當然爾地人工等化流管壁壓與偏前流向壓力﹝Pw =〈P+dP〉﹞,使得尤拉公式雖然根據動量原理推導出來,卻不是貨真價實的動量公式,以致於完全不能處理流場衝擊能損的狀況,並造成數值分析時陰魂不散地無理自動增能現象與相關嚴重的穩定/振盪問題!

這些致命而非常微妙的推導錯誤,雖然已經過兩百五十多年的嚴苛考驗都未被發現,讓流體動力學界長年活在類似斯德歌爾摩症候群痛苦掙扎的黑暗時代中,焦頭爛額地瞎忙著補破網,以致德國馮卡門流體動力研究院〈Von Karman Institute for Fluid Dynamics〉的著名學者S. Turek不禁坦誠吐露發人深省且最具代表性的心聲“We are very much embarrassed that we cannot solve even the simplest problem in fluid Dynamics”〈我們非常羞愧,因為我們甚至不能解出最簡單的流體動力問題〉。而上述極為重要的歷史性論文歷經多方穿透式的大模樣病理分析後,幡然提出回歸自然解除〈Pw=P+dP〉人工等化,近乎“淡定無為”卻劇力萬鈞的解決之道,加上極簡的柏努利因式分解,與解的存在/惟一之機鋒論述,也隱約散發出些許「空山松子落」的「幽幽禪意」。

 

National Chung-Hsing University's Hsing-juin Lee Discovers the Historical Fatal Derivation Error of Core Fluid Dynamics Equation System

Fluid dynamics is a very important academic area for the analysis and design of rocket, airplane, ship, submarine, automobile...and even the heart blood flow. Euler equation, derived in 1755, is the basis for general fluid dynamics analysis. Despite its sparkling elegance and sacrosanctity, while coming to theoretical analysis, it is doomed to encounter fatal existence/uniqueness problems, in addition to serious stability/oscillation problems in computational fluid dynamics (CFD) for modern age. For long years, these crucial problems frequently perplex the fluid dynamics academia.

The National Chung-Hsing University's research team of professor Hsing-juin Lee (including graduate students of mechanical engineering: Jiunn-Shean Chiang, Yu-Hsi Chih, Shu-Wei Wang, Ming-Fang Lu, and et al.) has recently published two papers in the prestigious“International Journal of Mechanical Engineering Education” i.e.“The Life and Death of Euler, Bernoulli, Navier-Stokes Equations and Associated CFD for So-called Incompressible Fluid Flow”〈 Vol.39.2〉 and“Inherent Numerical Discretization Dilemma Analysis of Euler Equation” 〈Vol.39.3〉. These papers have discovers the seemingly innocent but fatal error unawares embedded in the original derivation process of Euler equation ─ artificial equalization of crosswise and forward-biased streamwise pressures [Pw=P+dP]. Inevitably, this error will seriously affect associated Bernoulli and N-S equations too. Although derived by momentum principle, this disastrous error ingeniously renders the Euler equation to be a non-genuine momentum equation unable to accommodate any cases with possible energy loss. Moreover, this error also ghostly induces irrational energy-increase phenomenon, in addition to serious stability/oscillation problems for CFD. Then, should we blindly keep worshipping these non-genuine momentum equations forever?

Ironically, this slippery error has survived the scholastic scrutiny for more than 250 years and renders the fluid dynamics academia in the bitter struggle similar to Stockholm syndrome for a long dark age. In fact, the chastity of Euler and associated equations has long been contaminated by babysitting them desperately with many ad hoc artificial measures in order to get merely reluctant solutions. No wonder the famous scholar S. Turek of von Karman Institute for Fluid Dynamics once expressed the most impressive sound of his heart“We are very much embarrassed that we cannot solve even the simplest problem in fluid Dynamics”. Insightfully, after multiple-aspect strategic pathology analyses, the above very important historical papers conversely propose the back-to-nature neat resolution by relaxing the artificial equalization [Pw=P+dP] to dramatically cure this historical fatal error. Together, this amazing resolution, the very concise factorization of Bernoulli equation, and the judicious discussion on solution existence/uniqueness are sounding sort of "空山松子落" 的 "幽幽禪意"*

 

 

 

*Translation of the short Chinese sentence at end : the far-reaching Zen-taste of a falling pine cone in a vast/serene mountain.

 

 


 


  

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