单向色散波模型的有限体积方法
Finite volume methods for unidirectional dispersive wave models
AI总结：
将有限体积法扩展到一维色散单向水波传播，针对KdV-BBM型方程，采用显式和IMEX龙格-库塔时间离散，通过解析解验证并研究不变量守恒性质，应用于色散激波、孤立波及其相互作用等非线性现象。
摘要：
我们将有限体积法的框架扩展到一维空间中的色散单向水波传播。特别地，我们考虑了一种KdV-BBM型方程。显式和IMEX龙格-库塔型方法用于时间离散化。通过直接与解析解比较来验证全离散格式。还研究了不变量守恒性质。主要应用包括重要的非线性现象，如色散激波形成、孤立波及其各种相互作用。
英文摘要：
We extend the framework of the finite volume method to dispersive unidirectional water wave propagation in one space dimension. In particular we consider a KdV-BBM type equation. Explicit and IMEX Runge-Kutta type methods are used for time discretizations. The fully discrete schemes are validated by direct comparisons to analytic solutions. Invariants conservation properties are also studied. Main applications include important nonlinear phenomena such as dispersive shock wave formation, solitary waves and their various interactions.
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