Vladimir Andreevich Batishchev
Research interests:
Prof. Batishchev V.A. explores the processes of heat and mass transfer in the liquid layers of solid and free boundaries. These tasks are used in the field of space research. The effects of heat transfer are used for commercial purposes, such as in the preparation of drugs, biologics, in the separation of substances. Scientific work Batishcheva V.A. devoted to the study of thermo-capillary fluid flows. These problems have recently increased interest (regularly hosts international congresses and conferences). He studies the self-similar regimes of fluid flows with free boundaries, exploring new thermocapillary effects associated with the occurrence of the secondary modes by bifurcations. Batishchev V.A. established a new non-linear properties of the boundary layers near the boundaries of free (non-uniqueness, counter, self-induced pressure, etc.). He explores the new problems of thermogravitational boundary layers near the interface of liquid media. It is found that local cooling at the free surface may occur rotational flow regime heated liquid in a thin boundary layer. This effect can explain the process of such vortex structures, like a tornado. Developed methods used in the study of biomechanics short spiral waves in the aorta of humans and animals. The research results were published in journals priority Sciences, presented at international congresses and conferences.
Research projects:
- Research thermogravitational and thermo-capillary fluid flows. Calculations thermogravitational and thermocapillary convection. Fluid flow near the border section liquids, including near the free surfaces. Bifurcations heated liquid rotation at local cooling of the free surface. Application of the results to the problem of such vortex structures like a tornado. Application for Space Research. Application of heat transfer processes to the production of drugs, biologics, and the separation of substances.
- . The hydrodynamics of large blood vessels. Vortex flow of blood in the aorta of human and animals. Distribution short spiral waves in the aorta. Construction of mathematical models of swirling currents in the blood circulatory system of the body. Application of the results to the manufacturing heart problem.
Teaching:
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Turbulence Modeling.
We study the basic models of turbulence and methods of calculation of turbulent fluid flows. Presents semi-empirical models such as the k-e model, the turbulent diffusion, invariant modeling method, and others. We study the fundamentals of the spectral theory of turbulence. Studied modern numerical methods for calculating the turbulence. Presented examples of specific calculations of turbulent fluid flows.
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Asymptotical and numerical methods of hydrodynamics
Definitions and basic properties of the asymptotic series. Boundary layer method for linear and nonlinear boundary value problems. The averaging method in oscillating systems. WKB method and its application. Methods for conversion of non-uniform to uniform asymptotic series. Numerical methods in fluid dynamics. Classic algorithms - explicit and implicit methods, Crank-Nicholson method. The method of fractional steps, splitting method modified equations, group methods, and others. The finite element method for two-dimensional boundary value problems.
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The numerical solution of problems of applied mathematics
The method of "Cabaret" for linear differential equations. The basic algorithm and compared with the scheme Upwind LeapFrog. Conservation laws. Metod traveling waves. Dissipation and dispersion pattern. Nonlinear correction algorithm. Comparison with classical algorithms. Application to problems of convection and diffusion. The generalization to the nonlinear differential equations. Switching flows in a circuit. Calculation of uniform turbulence in the one-dimensional case. A generalization of the method to two-dimensional grids. Primenenie to the calculation of two-dimensional turbulence. Calculations of thermo-gravitational convection in a closed area
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Asymptotic methods of nonlinear hydrodynamics
Bifurcation of solutions of nonlinear boundary value problems. Branching self-similar solutions of the Navier-Stokes equations. Bifurcation of fluid flows in thin layers with a free and solid boundaries. The case of an inhomogeneous liquid. The emergence of the rotation in a liquid layer on cooling section liquid phase boundary. Stability in layers and viscous perfect fluid. The linearized problem. Stability Criteria for fluid flow.
