breaking of waves meaning in English
波浪破碎
Examples
- 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
当考虑粘性后，即在数学上反映为( 0 . 1 . 1 )中多了扩散项(二阶导数项) ，即使很粗糙的初始数据，解在瞬间内变的很光滑，这由于流体的粘性扩散引起，这种对流-扩散问题可用古典的微分方程来研究。自然的想法就是当粘性趋于零时，带粘性的对流-扩散问题的解在某意义下趋于无粘性问题( 0 . 1 . 1 )的解，这就是正则化方法。另一办法从离散(数值)角度上研究仅有对流项的守恒律( 0 . 1 . 1 ) ，如构造它的差分格式，甚至更一般的有限体积格式，有限元及谱方法等，从这些格式构造近似解(常表现为分片多项式)来逼近原守恒律的解。