A Numerical Scheme for Wave Turbulence: 3-Wave Kinetic Equations

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. Up to our knowledge, this is the first numerical scheme that could 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 the theoretical one obtained by Soffer and Tran. Our finite volume algorithm relies on a new identity, that allows one to reduce the number of terms needed to be approximated in the collision operators.