Research output: Contribution to journal › Article › peer-review
Algorithm for Solving the Four-Wave Kinetic Equation in Problems of Wave Turbulence. / Semisalov, B. V.; Medvedev, S. B.; Nazarenko, S. V. et al.
In: Computational Mathematics and Mathematical Physics, Vol. 64, No. 2, 08.04.2024, p. 340-361.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 61238850