Numerical Schemes for 3-Wave Kinetic Equations: A Complete Treatment of the Collision Operator
Abstract
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. We then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.17481
- arXiv:
- arXiv:2402.17481
- Bibcode:
- 2024arXiv240217481W
- Keywords:
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- Mathematics - Numerical Analysis