Valentin Tenenev
Doctor of Physics and Mathematics, Professor
Born: September 11, 19491971: graduation from the Faculty of Physics and Engineering, Tomsk State University
19721988: Junior Research Worker and then Head of Laboratory in the research and production association “Altai”
1983: earned the degree of Candidate of Engineering
1986: received the title of Senior Research Worker
1993: earned the degree of Doctor of Physics and Mathematics
1997: Professor at the Department of Mathematical Modeling of Physical Processes
Since 1989 he has been Professor at the Department of Higher Mathematics, Kalashnikov Izhevsk State Technical University.
Research supervision of 4 Doctors of Science and 22 Candidates of Science.
Honorary Professor at the Izhevsk State Technical University, Honored Employee of Higher School of the Russian Federation.
Master of Sports in Mountaineering.
V.A. Tenenev specializes in the mathematical modeling of multiphase reactive flows in power plants using numerical methods. He works in an area where intelligent algorithms are applied in modeling complex systems.
Publications:
Rusyak I. G., Tenenev V. A., Korolev S. A.
Numerical Simulation of the Nonstationary Process of the Shot Based on the Navier – Stokes Equations
2022, Vol. 18, no. 3, pp. 333348
Abstract
This paper gives a spatial mathematical formulation of the problem of internal ballistics
based on the Navier – Stokes equations, taking into account the swirl of the flow due to the
rotation of the projectile. The ke model of turbulent viscosity is used. The control volume
method is used for the numerical solution of systems of equations. The gas parameters at
the boundaries of the control volumes are determined by the method of S. K. Godunov using
a selfsimilar solution to the problem of the decay of an arbitrary discontinuity. The MUSCL
scheme is used to increase the order of approximation of the difference method. For equations
written in a cylindrical coordinate system, an orthogonal difference grid is constructed using
the complex boundary element method. A comparative analysis of the results obtained with
different approaches to modeling the process of an artillery shot is given. Quantitative data are
presented on the influence of factors not previously taken into account on the characteristics of
the process.

Shaura A. S., Tenenev V. A., Vetchanin E. V.
The Problem of Balancing an Inverted Spherical Pendulum on an Omniwheel Platform
2021, Vol. 17, no. 4, pp. 507525
Abstract
This paper addresses the problem of balancing an inverted pendulum on an omnidirectional
platform in a threedimensional setting. Equations of motion of the platform – pendulum system
in quasivelocities are constructed. To solve the problem of balancing the pendulum by controlling
the motion of the platform, a hybrid genetic algorithm is used. The behavior of the system is
investigated under different initial conditions taking into account a necessary stop of the platform
or the need for continuation of the motion at the end point of the trajectory. It is shown that
the solution of the problem in a twodimensional setting is a particular case of threedimensional
balancing.

Raeder T., Tenenev V. A., Chernova A. A.
Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures
2021, Vol. 17, no. 2, pp. 195209
Abstract
This paper is concerned with assessing the correctness of applying various mathematical
models for the calculation of the hydroshock phenomena in technical devices for modes close to
critical parameters of the fluid. We study the applicability limits of the equation of state for
an incompressible fluid (the assumption of constancy of the medium density) to the simulation
of processes of the safety valve operation for high values of pressures in the valve. We present
a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible
fluids. A generalization of the method for the Mie – Grüneisen equation of state is made
using an algorithm of local approximation. A detailed validation and verification of the developed
numerical method is provided, and relevant schemes and algorithms are given. Modeling of
the hydroshock phenomenon under the valve actuation within the incompressible fluid model is
carried out by the openFoam software. The comparison of the results for the weakly compressible
and incompressible fluid models allows an estimation of the applicability ranges for the proposed
schemes and algorithms. It is shown that the problem of the hydroshock phenomenon is correctly
solved using the model of an incompressible fluid for the modes characterized by pressure ratios of
no more than 1000 at the boundary of media discontinuity. For all pressure ratios exceeding 1000,
it is necessary to apply the proposed weakly compressible fluid approach along with the Mie –
Grüneisen equation of state.

Raeder T., Tenenev V. A., Koroleva M. R., Mishchenkova O. V.
Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State
2021, Vol. 17, no. 1, pp. 119138
Abstract
The paper presents a modification of the digital method by S. K. Godunov for calculating
real gas flows under conditions close to a critical state. The method is generalized to the case of
the Van der Waals equation of state using the local approximation algorithm. Test calculations
of flows in a shock tube have shown the validity of this approach for the mathematical description
of gasdynamic processes in real gases with shock waves and contact discontinuity both in areas
with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with
local approximation of the Van der Waals equation by a twoterm equation of state was used for
simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex
shape, which is characteristic of the internal space of a safety valve. We have demonstrated that,
under nearcritical conditions, areas of nonclassical gas behavior may appear, which affects the
nature of flows. We have studied nonlinear processes in a safety valve arising from the movement
of the shutoff element, which are also determined by the device design features and the gas
flow conditions.

Mamaev I. S., Tenenev V. A., Vetchanin E. V.
Dynamics of a Body with a Sharp Edge in a Viscous Fluid
2018, Vol. 14, no. 4, pp. 473494
Abstract
This paper addresses the problem of planeparallel motion of the Zhukovskii foil in a viscous
fluid. Various motion regimes of the foil are simulated on the basis of a joint numerical solution
of the equations of body motion and the Navier – Stokes equations. According to the results
of simulation of longitudinal, transverse and rotational motions, the average drag coefficients
and added masses are calculated. The values of added masses agree with the results published
previously and obtained within the framework of the model of an ideal fluid. It is shown that
between the value of circulation determined from numerical experiments, and that determined
according to the model of and ideal fluid, there is a correlation with the coefficient $\mathcal{R} = 0.722$.
Approximations for the lift force and the moment of the lift force are constructed depending
on the translational and angular velocity of motion of the foil. The equations of motion of
the Zhukovskii foil in a viscous fluid are written taking into account the found approximations and the drag coefficients. The calculation results based on the proposed mathematical model
are in qualitative agreement with the results of joint numerical solution of the equations of body
motion and the Navier – Stokes equations.

Tenenev V. A., Vetchanin E. V., Ilaletdinov L. F.
Chaotic dynamics in the problem of the fall of a screwshaped body in a fluid
2016, Vol. 12, No. 1, pp. 99120
Abstract
This paper is concerned with the process of the free fall of a threebladed screw in a fluid. The investigation is performed within the framework of theories of an ideal fluid and a viscous fluid. For the case of an ideal fluid the stability of uniformly accelerated rotations (the Steklov solutions) is studied. A phenomenological model of viscous forces and torques is derived for investigation of the motion in a viscous fluid. A chart of Lyapunov exponents and bifucation diagrams are computed. It is shown that, depending on the system parameters, quasiperiodic and chaotic regimes of motion are possible. Transition to chaos occurs through cascade of perioddoubling bifurcations.

Ramodanov S. M., Tenenev V. A., Treschev D. V.
Selfpropulsion of a body with rigid surface and variable coefficient of lift in a perfect fluid
2012, Vol. 8, No. 4, pp. 799813
Abstract
We study the system of a 2D rigid body moving in an unbounded volume of incompressible, vortexfree perfect fluid which is at rest at infinity. The body is equipped with a gyrostat and a socalled Flettner rotor. Due to the latter the body is subject to a lifting force (Magnus effect). The rotational velocities of the gyrostat and the rotor are assumed to be known functions of time (control inputs). The equations of motion are represented in the form of the Kirchhoff equations. In the case of piecewise continuous controls, the integrals of motion are indicated. Using these integrals we obtain a (reduced) system of firstorder differential equations on the configuration space. An optimal control problem for several types of the inputs is then solved using genetic algorithms.

Vetchanin E. V., Mamaev I. S., Tenenev V. A.
The motion of a body with variable mass geometry in a viscous fluid
2012, Vol. 8, No. 4, pp. 815836
Abstract
An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier–Stokes equations and equations of motion. A nonstationary threedimensional solution to the problem is found. The motion of a sphere and a dropshaped body in a viscous fluid, which is caused by the motion of internal material points, in a gravitational field is explored. The possibility of motion of a body in an arbitrary given direction is shown.

Ramodanov S. M., Tenenev V. A.
Motion of a body with variable distribution of mass in a boundless viscous liquid
2011, Vol. 7, No. 3, pp. 635647
Abstract
In the paper we consider the motion of a rigid body in a boundless volume of liquid. The body is set in motion by redistribution of internal masses. The mathematical model employs the equations of motion for the rigid body coupled with the hydrodynamic Navier–Stokes equations. The problem is mostly dealt with numerically. Simulations have revealed that the body’s trajectory is strongly governed by viscous effects.
