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

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

Journal

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662

Output data

Year: 2024, Volume: 64, Number: 2, Pages: 340-361 Pages count : 22 DOI: 10.1134/s0965542524020118

Tags

wave turbulence, kinetic equation, nonlinear interaction of waves, calculation of collision integral, singular point, cubature formula, exponential convergence, rational approximation, adaptive method, collocation method, relaxation method, nonlinear Schrödinger equation, Bose–Einstein condensation, deep-water waves

Authors

Semisalov B.V. ^1,2,4 , Medvedev S.B. ^2,4 , Nazarenko S.V. ³ , Fedoruk M.P. ^2,4

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia
2	Federal Research Center for Information and Computational Technologies, 630090, Novosibirsk, Russia
3	Université Côte d'Azur, CNRS, Institut de Physique de Nice (INPHYNI), 06200, Nice, France
4	Novosibirsk State University, Novosibirsk, 630090 Russia

Funding (1)

Russian Science Foundation

22-11-00287

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.

Semisalov B.V. , Medvedev S.B. , Nazarenko S.V. , Fedoruk M.P.
Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence
Computational Mathematics and Mathematical Physics. 2024. V.64. N2. P.340-361. DOI: 10.1134/s0965542524020118 WOS Scopus РИНЦ OpenAlex

Семисалов Б.В. , Медведев С.Б. , Назаренко С.В. , Федорук М.П.
Алгоритм решения четырехволнового кинетического уравнения в задачах волновой турбулентности
Журнал вычислительной математики и математической физики. 2024. Т.64. №2. С.364-386. DOI: 10.31857/S0044466924020136 РИНЦ OpenAlex

Submitted:	Jun 29, 2023
Accepted:	Oct 20, 2023
Published print:	Apr 1, 2024
Published online:	Apr 1, 2024

Web of science:	WOS:001195395200012
Scopus:	2-s2.0-85189301766
Elibrary:	66775415
OpenAlex:	W4393377679

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