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Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence

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Abstract

We propose the method for numerical solution of four-wave kinetic equations that arise in the wave turbulence (weak turbulence) theory when describing a homogeneous isotropic interaction of waves. To calculate the collision integral in the right-hand side of equation, the cubature formulas of high rate of convergence are developed, which allow for adaptation of the algorithm to the singularities of the solutions and of the integral kernels. The convergence tests in the problems of integration arising from real applications are done. To take into account the multi-scale nature of turbulence problems in our algorithm, rational approximations of the solutions and a new time marching scheme are implemented and tested. The efficiency of the developed algorithm is demonstrated by modelling the inverse cascade of Bose gas particles during the formation of a Bose–Einstein condensate.

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Funding

This work was supported by the Russian Science Foundation (agreement no. 22-11-00287).

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    B. V. Semisalov

  2. Federal Research Center for Information and Computational Technologies, 630090, Novosibirsk, Russia

    B. V. Semisalov, S. B. Medvedev & M. P. Fedoruk

  3. Novosibirsk State University, 630090, Novosibirsk, Russia

    B. V. Semisalov, S. B. Medvedev & M. P. Fedoruk

  4. Université Côte d’Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06200, Nice, France

    S. V. Nazarenko

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  1. B. V. Semisalov
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  2. S. B. Medvedev
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  3. S. V. Nazarenko
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  4. M. P. Fedoruk
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Correspondence to B. V. Semisalov.

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Translated by E. Chernokozhin

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Semisalov, B.V., Medvedev, S.B., Nazarenko, S.V. et al. Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence. Comput. Math. and Math. Phys. 64, 340–361 (2024). https://doi.org/10.1134/S0965542524020118

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