hyperbolic shock 中文意思是什麼
hyperbolic shock
解釋
雙曲線激波- hyperbolic : adj. 【數學】雙曲線的。adv. -ically adj. 誇張法的。
- shock : n 1 沖突；沖撞；沖擊；突擊。2 震動；沖動；激動。3 感動；憤慨；驚愕；震驚。4 地震。5 【醫學】休克...
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This feature reflects the physical phenomenon of breaking of waves and development of shock waves. in the fields of fulid dynamics, ( 0. 2. 1 ) is an approximation of small visvosity phenomenon. if viscosity ( or the diffusion term, two derivatives ) are added to ( 0. 2. 1 ), it can be researched in the classical way which say that the solutions become very smooth immediately even for coarse inital data because of the diffusion of viscosity. a natural idea ( method of regularity ) is obtained as follows : solutions of the viscous convection - diffusion pr oblem approachs to the solutions of ( 0. 2. 1 ) when the viscosity goes to zeros. another method is numerical method such as difference methods, finite element method, spectrum method or finite volume method etc. numerical solutions which is constructed from the numerical scheme approximate to the solutions of the hyperbolic con - ervation laws ( 0. 2. 1 ) as the discretation parameter goes to zero. the aim of these two methods is to construct approximate solutions and then to conside the stability of approximate so - lutions ( i, e. the upper bound of approximate solutions in the suitable norms, especally for that independent of the approximate parameters ). using the compactness framework ( such as bv compactness, l1 compactness and compensated compactness etc ) and the fact that the truncation is small, the approximate function consquence approch to a function which is exactly the solutions of ( 0. 2. 1 ) in some sense of definiton
當考慮粘性后，即在數學上反映為（ 0 . 1 . 1 ）中多了擴散項（二階導數項） ，即使很粗糙的初始數據，解在瞬間內變的很光滑，這由於流體的粘性擴散引起，這種對流-擴散問題可用古典的微分方程來研究。自然的想法就是當粘性趨于零時，帶粘性的對流-擴散問題的解在某意義下趨于無粘性問題（ 0 . 1 . 1 ）的解，這就是正則化方法。另一辦法從離散（數值）角度上研究僅有對流項的守恆律（ 0 . 1 . 1 ） ，如構造它的差分格式，甚至更一般的有限體積格式，有限元及譜方法等，從這些格式構造近似解（常表現為分片多項式）來逼近原守恆律的解。 -
From the experiments in hyperbolic conservation laws, we can see that if we only use high resolution shock capturing method in scalar equation, there would have a transition near the interface ; but when coupled with level set method, we can get a sharp interface, the interface is tracked exactly
通過實驗可以看出，對標量雙曲守恆律方程應甩levelset方法后，我們得到了銳利的圖像，界面得到了準確追蹤，而不像高解析度激波捕捉方法，在界面附近有一個過渡區域。 -
In this thesis, we couple high resolution shock capturing method and level set method to compute hyperbolic conservation laws
本文將高解析度激波捕捉格式與levelset方法結合起來計算雙曲守恆律方程（組） 。
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