We introduce a finite volume scheme to solve 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 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:我们引入一个数量有限的计划来解决异向3波动动方程式问题。 我们用关于能源长期行为的理论结果来测试我们的数字解决方案, 并观察我们的解决方案可以验证能源级联现象。 据我们所知,这是第一个可以捕捉长期无症状的解决异向3波动动方程式的方法, 在那里可以观察到能源级联。 我们的数字能源级联率与先前获得的理论结果非常一致。 这里给出的数量级计划依赖于新的身份, 允许一个人减少碰撞操作者所需的条件数量 。</s>