TY - JOUR

T1 - Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence

AU - Semisalov, B. V.

AU - Medvedev, S. B.

AU - Nazarenko, S. V.

AU - Fedoruk, M. P.

N1 - This work was supported by the Russian Science Foundation (agreement no. 22-11-00287).

PY - 2024/4/8

Y1 - 2024/4/8

N2 - 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.

AB - 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.

KW - Bose–Einstein condensation

KW - adaptive method

KW - calculation of collision integral

KW - collocation method

KW - cubature formula

KW - deep-water waves

KW - exponential convergence

KW - kinetic equation

KW - nonlinear Schrödinger equation

KW - nonlinear interaction of waves

KW - rational approximation

KW - relaxation method

KW - singular point

KW - wave turbulence

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001195395200012

UR - https://www.mendeley.com/catalogue/79421eaa-68f8-3dfc-8022-b93a211c8c47/

U2 - 10.1134/S0965542524020118

DO - 10.1134/S0965542524020118

M3 - Article

VL - 64

SP - 340

EP - 361

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 2

ER -