We introduce a finite volume scheme to solve a special case of isotropic 3-wave kinetic equations. We test our numerical solution against theoretical results concerning the long time behavior of the energy and observe that our solutions verify the energy cascade phenomenon. To our knowledge, this is the first numerical scheme that can capture the long time asymptotic behavior of solutions to those isotropic 3-wave kinetic equations, where the energy cascade can be observed. Our numerical energy cascade rates are in good agreement with previously obtained theoretical results. The finite volume scheme given here relies on a new identity, allowing one to reduce the number of terms needed in the collision operators.

翻译：我们提出了一种有限体积格式，用于求解各向同性三波动力学方程的特例。我们将数值解与关于能量长时间行为的理论结果进行对比，观察到我们的解验证了能量级联现象。据我们所知，这是首个能够捕获这些各向同性三波动力学方程解长时间渐近行为（并可观测到能量级联）的数值格式。我们的数值能量级联速率与先前获得的理论结果吻合良好。本文提出的有限体积格式基于一个新的恒等式，该恒等式能够减少碰撞算子中所需项的数量。