数值Rosenau-Hyman紧致子的自相似辐射
Self-similar Radiation from Numerical Rosenau-Hyman Compactons
摘要：
具有紧支撑的孤立波的数值模拟的特征在于伪现象的存在，如数值感应辐射，这里使用应用于Rosenau-Hyman K（p，p）方程的四种数值方法来说明。前向辐射和后向辐射都是从具有自相似形状的光子发射的，这已经通过适当的比例图示出。网格细化研究表明，辐射的幅度随着网格尺寸的减小而减小，从而证实了其数值起源。研究了两种辐射的波前速度和振幅随湍流和数值参数的变化关系。辐射的振幅随时间呈指数下降，其特征在于具有几乎恒定的标度指数。本文的数值结果表明，后向辐射和前向辐射都对应于一个标度指数自相似函数。
英文摘要：
The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the Rosenau-Hyman K(p,p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.
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