Open AccessDisconnected stationary solutions for 3D Kolmogorov flow problem: preliminary results
Author(s) -
Н. М. Евстигнеев
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012046
Subject(s) - mathematics , torus , mathematical analysis , flow (mathematics) , spectral method , nonlinear system , projection (relational algebra) , fourier transform , bifurcation , arc length , arc (geometry) , geometry , physics , algorithm , quantum mechanics
The extension of the classical A.N. Kolmogorov’s flow problem for the stationary 3D Navier-Stokes equations on a stretched torus for velocity vector function is considered. A spectral Fourier method with the Leray projection is used to solve the problem numerically. The resulting system of nonlinear equations is used to perform numerical bifurcation analysis. The problem is analyzed by constructing solution curves in the parameter-phase space using previously developed deflated pseudo arc-length continuation method. Disconnected solutions from the main solution branch are found. These results are preliminary and shall be generalized elsewhere.