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840 Section 1
tude and phase problems are modeled by corresponding nonlinear singular integral equations. In the two.dimensional case amplitude and phase problems are modeled by corresponding nonlinear bisingular integral equations. Several approaches are presented for modeling two.dimensional problems:
1) reduction of amplitude and phase problems to systems of nonlinear singular integral equations;
2) using methods of the theory of functions of the complex variable, problems are reduced to nonlinear bisingular integral equations.
To solve the constructed nonlinear singular equations, methods of collocation and mechanical quadrature are used. These methods lead to systems of nonlinear algebraic equations, which are solved by the continuous method for solution of nonlinear operator equations. The choice of this method is due to the fact that it is sta�ble against perturbations of coefficients in the right.hand side of the system of equations. In addition, the method is realizable even in cases where the Frechet and Gateaux derivatives degenerate at a finite number of steps in the iterative process.
Some modelexamples have shown effectiveness of proposed methods and numerical algorithms.
Numericalsimulationofthedynamicsofaheatedturbulentmixingzoneinalinearstratifiedmedium
G. G. Chernykh1,2, A. V. Fomina3, N. P. Moshkin2,4
1Federal Research Center for Information and ComputationalTechnologies 2Novosibirsk State University 3Novokuznetsk Institute (branch)of the Kemerovo State University, Novokuznetsk 4Lavrentyev Institute of Hydrodynamics SB RAS Email: [email protected], [email protected], [email protected]
DOI 10.24412/cl.35065.2021.1.00.10
Evolution oflocalized regions of turbulized fluid (turbulent spots)has a decisive effect on the formation of fine microstructure of hydrophysical fields in the ocean [1].
Based on an algebraic model of Reynolds stresses and fluxes, a numerical model of the dynamics of a flat localized region of turbulent perturbations of non.zero buoyancy in a linearly stratified medium was con�structed. Presence of non.zero buoyancy leads to increase in the geometricaldimensions of the turbulent spot and generation of internalwaves of greater amplitude in comparison with a spot of non.zero buoyancy. The work is a continuation and development of research [2].
References
1.
Monin A. S., Yaglom A. M. Statistical fluid mechanics. V. 1. Mechanics of turbulence. Dover Books on Physics. 2007, 784 p.
2.
Chernykh G. G., Fomina A. V., Moshkin N. P. Numerical Simulation of Dynamics of Weakly Heated Turbulent Mixing Zone in Linearly Stratified Medium // J. of EngineeringThermophysics. 2020. Vol.29.Iss. 4. P. 674.685.
A.WENOschemesbasedonadaptiveartificialviscosity
S. Chu, A. Kurganov
Southern University of Science and Technology, Shenzhen, China Email: [email protected]
DOI 10.24412/cl.35065.2021.1.00.11
We will introduce new finite.difference A.WENO schemes for hyperbolic systems of conservation laws. The proposed schemes are fifth.order accurate in space and stable. Unlike the original A.WENO schemes [1], the stabilization is achieved using the adaptive artificial viscosity (AAV) approach introduced in [3]: the AAV
