Yuri Mikhailovich Nechepurenko

• PhD, Prof.
• Researcher at Institute of Numerical Mathematics, Russian Academy of Sciences

Modern approaches to visualization and automatic identification of separation regionsof three-dimensional boundary layers are discussed. The corresponding algorithms are implemented within the framework of the original LOTRAN software package designed to predict the onset of a laminar-turbulent transition in boundary layers over small-curvature sur...

A technology for numerical analysis of the local biglobal stability of laminar incompressible boundary layers over streamwise-ribbed surfaces is proposed. Within its framework, the stability is studied using the locally-parallel approximation and Floquet theory. The work of the proposed technology is demonstrated by the example of a boundary layer...

In this work, we search for the conditions for the occurrence of long COVID using the recently developed COVID-19 disease dynamics model which is a system of delay differential equations. To do so, we search for stable stationary or periodic solutions of this model with low viral load that can be interpreted as long COVID using our recently develop...

Работа посвящена численному анализу чувствительности характеристик пространственной устойчивости пограничных слоев к погрешностям, с которыми задано основное течение. Предлагается использовать для этого структурированные псевдоспектры. Показано, что полученные оценки значительно точнее оценок на основе обычного псевдоспектра. Изложение ведется на п...

The problem of generating the Tollmien-Schlichting waves (leading eigenmodes) and optimal disturbances with a given accuracy using optimal blowing–suction is considered with the example of Poiseuille flow in a duct of square cross-section and streamwise-harmonic blowing-suction through the duct walls. The problem is reduced to solving optimal contr...

The work is devoted to modeling the disturbance propagation in viscous incompressible laminar boundary layers, using linearized equations for disturbance amplitudes. Along with the numerical model based on original linearized equations, the article considers three models based on equations derived from the original ones by neglecting the streamwise...

Optimal disturbances of the periodic solution of the hepatitis B dynamics model corresponding to the chronic recurrent form of the disease are found. The dependence of the optimal disturbance on the phase of periodic solution is analyzed. Four phases of the solution are considered, they correspond to clinically different periods of development of t...

This work is devoted to a numerical analysis of the sensitivity of the spatial stability characteristics of boundary layers to uncertainties of the main flow. It is proposed to use structured pseudospectra for this purpose. It is shown that the obtained estimates are much more accurate than estimates based on an unstructured pseudospectrum. The pre...

An original numerical matrix algorithm aimed at solving the optimal control problems for linear systems of ordinary differential equations with constant coefficients is proposed. The work of the algorithm is demonstrated with the problem, which consists in generating a given small disturbance of the Poiseuille flow in an infinite duct by blowing an...

This work is devoted to the technology developed by the authors that allows one for fixed values of parameters and tracing by parameters to calculate stationary solutions of systems with delay and analyze their stability. We discuss the results of applying this technology to the Marchuk–Petrov antiviral immune response model with parameter values c...

The hydrodynamic stability theory deals with external disturbances of a main flow, whose stability is of interest. It studies their propagation in space or evolution in time. Stability characteristics, such as the growth rate, and the phase and group velocities, allow one to describe the propagation of the most unstable disturbances. The computatio...

Optimal disturbances of a number of typical stationary solutions of the hepatitis B virus infection dynamics model have been found. Specifically optimal disturbances have been found for stationary solutions corresponding to various forms of the chronic course of the disease, including those corresponding to the regime of low-level virus persistence...

The article deals with the downstream propagation of small–amplitude disturbances of viscous incompressible laminar boundary layers, using the linearized equations for disturbance amplitudes. Two different methods are proposed. The first one solves a two-dimensional boundary-value problem, using a buffer-domain technique to mimic the outflow bounda...

The infectious disease caused by human immunodeficiency virus type 1 (HIV-1) remains a serious threat to human health. The current approach to HIV-1 treatment is based on the use of highly active antiretroviral therapy, which has side effects and is costly. For clinical practice, it is highly important to create functional cures that can enhance im...

The paper is focused on the dependence of optimal disturbances of stable periodic solutions of time-delay systems on phases of such solutions. The results of numerical experiments with the well-known model of the dynamics of infection caused by lymphocytic choriomeningitis virus are presented and discussed. A new more efficient method for computing...

The results of numerical simulation of a subsonic flow around a 45-degree swept wing model with a NACA 67 1-215 airfoil are considered. The simulation was performed using the ANSYS Fluent package with a plug-in original module LOTRAN for predicting the position of laminar-turbulent transition, which implements the eN-method. In particular, the dist...

In this work, we briefly describe our technology developed for computing periodic solutions of time-delay systems and discuss the results of computing periodic solutions for the Marchuk-Petrov model with parameter values, corresponding to hepatitis B infection. We identified the regions in the model parameter space in which an oscillatory dynamics...

This work is devoted to the technology developed by the authors that allows one for fixed values of parameters and tracing by parameters to calculate stationary solutions of systems with delay and analyze their stability. We discuss the results of applying this technology to Marchuk-Petrov's antiviral immune response model with parameter values cor...

Optimal disturbances of a turbulent stably stratified plane Couette flow in a wide range of Reynolds and Richardson numbers are studied. These disturbances are computed based on a simplified system of equations in which turbulent Reynolds stresses and heat fluxes are approximated by isotropic viscosity and diffusivity with the coefficients obtained...

A concept of optimal disturbances of periodic solutions for a system of time-delay differential equations is defined. An algorithm for computing the optimal disturbances is proposed and justified. This algorithm is tested on the known system of four nonlinear time-delay differential equations modelling the dynamics of the experimental infection cau...

The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical syst...

This work is devoted to the constant (time-independent) upper bounds on the function ∥ exp( tA )∥ 2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper boun...

Systems of time-delay differential equations are widely used to study the dynamics of infectious diseases and immune responses. The Marchuk-Petrov model is one of them. Stable non-trivial steady states and stable periodic solutions to this model can be interpreted as chronic viral diseases. In this work we briefly describe our technology developed...

Large-scale inclined organized structures in stably stratified turbulent shear flows were revealed in the numerical simulation and indirectly confirmed by the field measurements in the stable atmospheric boundary layer. Spatial scales and forms of these structures coincide with those of the optimal disturbances of a simplified linear model. In this...

The goal of the paper is to determine the position of the laminar-turbulent transition in the boundary layer of a prolate spheroid using the e N -method with the calibration of threshold N -factors. It is demonstrated that the predicted and experimental data on the laminarturbulent transition are in good agreement.

In this paper, known probabilistic methods for estimating the thickness of the boundary layer of a two-dimensional laminar flow of viscous incompressible fluid are extended to three-dimensional laminar flows of a viscous compressible medium. Their applicability to the problems of boundary-layer stability is studied with the LOTRAN3 software package...

The paper describes a technology designed for computing three-dimensional transonic laminar–turbulent flows at various aerodynamic configurations with the use of the general-purpose computational fluid dynamics code ANSYS Fluent and an integrated special module of computing the laminar–turbulent transition position created on the basis of the auton...

The problem of calibration of semi-empirical eN-method for prediction of laminar-turbulent transition in three-dimensional boundary layers is discussed. A high-resolving panoramic experimental technique to estimate the onset and length of the transition for aerodynamic applications is proposed and described. The position of laminar-turbulent transi...

The paper is focused on computation of stable periodic solutions to systems of delay differential equations modelling the dynamics of infectious diseases and immune response. The method proposed here is described by an example of the well-known model of dynamics of experimental infection caused by lymphocytic choriomeningitis viruses. It includes t...

In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential equations with delayed independent variables. We develop the method for calculation of perturbations of the initial state of a dynamical system with delayed independent variable producing maximal amplifi...

Actual fundamental and computational problems of laminar–turbulent transition prediction in aerodynamic flows are discussed. The author’s approach based on the exp(N)-method is briefly described. The results of experimental studies aimed at clarifying the calibration of the exp(N)-method is highlighted. Particularly, one of the main problem is a li...

Modern fundamental and computational problems in predicting the laminar-turbulent transition in aerodynamic flows are considered. A review of advanced engineering methods of forecasting the transition to turbulence in two- and three-dimensional aerodynamic flows at pre- and transonic speeds is given. The approach based on the exp (N)-method is summ...

A transition prediction module for 3D compressible flows was developed by the authors in order to include the prediction of the laminar-turbulent transition in hydrodynamics computational codes; particularly the module was integrated in the general-purpose gas-dynamic package ANSYS Fluent. The subsonic air flow about a swept wing model with the swe...

The paper illustrates some result of the efforts in ITAM SB RAS in designing an engineering tool LOTRAN 3.0 integrated with the ANSYS Fluent for predicting the position of the laminar-turbulent transition in compressible fully three-dimensional boundary layers. The paper presents some validation results for the laminar- turbulent transition in full...

The problem of guaranteed computation of all steady states of the Marchuk–Petrov model with fixed values of parameters and analysis of their stability are considered. It is shown that the system of ten nonlinear equations, nonnegative solutions of which are steady states, can be reduced to a system of two equations. The region of possible nonnegati...

Direct numerical simulation data of a stratified turbulent Couette flow contains two types of organized structures: rolls arising at neutral and close to neutral stratifications, and layered structures which manifest themselves as static stability increases. It is shown that both types of structures have spatial scales and forms that coincide with...

A subsonic (U ∞ =30 m/s) flow around a swept wing with a sweep angle of 45° and a chord of 700 mm aligned at an angle of attack in the test section of the T-324 wind tunnel based at the Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences is considered. The experiments include measu...

The goal of the paper is to determine the position of the laminar-turbulent transition in subsonic and transonic two-dimensional boundary layers on an airfoil with the use of the a laminar-turbulent transition module based on the e N -method and using the results of numerical simulations of the laminar flow around the model performed by the ANSYS F...

The paper deals with the numerical simulation of the laminar-turbulent transition as the gas flow moves at a nacelle at transonic speeds. The laminar-turbulent transition position in the 3D boundary layer of the nacelle is found with the aid of the laminar-turbulent transition module based on the e N -method which involves the data of the numerical...

The study is aimed at determining the position of the laminar-turbulent transition in subsonic and transonic two-dimensional boundary layers with the use of a novel software package LOTRAN 2.0 developed by the authors. The package is based on the eN-method and employs numerical data of numerical simulations of the laminar flow performed by standard...

Direct numerical simulation data of a stably stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral stratification, and the layered structures, which manifest themselves as the static stability increases. It is shown that both types of structures have spatial scales and for...

The inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of t...

The goal of the present work is to integrate the LOTRAN 3.0 package designed for computing the laminar-turbulent transition on the basis of the eN-method into the ANSYS Fluent fluid dynamic software. Integration means the transformation of this package into a laminar-turbulent transition module, i.e., the development and implementation of interface...

A review of recent research on the hydrodynamic instabilities of incompressible asymmetric flows along dihedral corner with the aim of obtaining data necessary for modeling the laminar-turbulent transition is presented. The results of numerical simulation of the flow along the corner based on parametric (for various angles of attack and for differe...

Direct numerical simulation data of a stably stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral stratification and the layered structures that manifest themselves as the static stability increases. It is shown that both types of structures have spatial scales and forms...

Novel fast algorithms for computing the maximum amplification of the norm of solution and optimal disturbances for delay systems are proposed and justified. The proposed algorithms are tested on a system of four nonlinear delay differential equations providing a model for the experimental infection caused by the lymphocytic choriomeningitis virus (...

The work is devoted to the use of asymptotic boundary conditions for engineering prediction of the laminar-turbulent transition position in hydrodynamic flows by the eN-method. It is shown that the asymptotic boundary conditions can significantly reduce the total computational cost.

A new approach to formulation of asymptotic boundary conditions for eigenvalue problems arising in numerical analysis of hydrodynamic stability of such shear flows as boundary layers, separations, jets, wakes, characterized by almost constant velocity of the main flow outside the shear layer or layers is proposed and justified. This approach makes...

Direct numerical simulation data of a stratified turbulent Couette flow contains two types of organized structures: the rolls that arise at neutral and close to neutral stratification, and the layered structures, which manifest themselves as the static stability increases. It is shown that both types of structures have spatial scales and forms that...

Two methods of laminar-turbulent transition prediction are compared in application to transonic flow on an airfoil. An attempt was made to use LST and eN method for calculating the transition position based on the mean flow obtained with the help of ANSYS Fluent. Two-dimensional flow around RAE (NPL) 5212 airfoil was considered for M∞=0.5 and M∞=0....

Inviscid instability of nonsymmetric self-similar incompressible axial corner-layer flow at zero streamwise pressure gradient is considered. It is shown that the leading corner mode exhibits the maximum growth at least in a certain range of the streamwise wave number, outside of which the growth is overlapped by boundary-layer modes. The maximum gr...

For bistable time-delay dynamical systems modeling the dynamics of viral infections and the virusinduced immune response, an efficient approach is proposed for constructing optimal disturbances of steady states with a high viral load that transfer the system to a state with a low viral load. Functions approximating the behavior of drugs within the...

A technique for analyzing the spatial stability of viscous incompressible shear flows in ducts of constant cross section, i.e., a technique for the numerical analysis of the stability of such flows with respect to small time-harmonic disturbances propagating downstream is described and justified. According to this technique, the linearized equation...

Symmetric and asymmetric self-similar flows of a viscous incompressible fluid along a semi-infinite right-angle dihedral corner with a preset streamwise pressure gradient have been considered. Equations describing such flows in the framework of boundary layer approximation have been derived. The asymptotic behavior of solutions of the derived equat...

The block inverse iteration and block Newton’s methods proposed by the authors of this paper for computing invariant pairs of regular linear matrix pencils are generalized to the case of regular nonlinear matrix pencils. Numerical properties of the proposed methods are demonstrated with a typical quadratic eigenproblem.

In this paper, we apply optimal perturbations to control mathematical models of infectious diseases expressed as systems of nonlinear differential equations with delayed argument. We develop the method for calculation of perturbations of the initial state of a dynamical system with delayed argument producing maximal amplification in the given local n...

A new method for constructing the multi-modal impacts on the immune systemin the chronic phase of viral infection, based on mathematical models formulated with delay-differential equations is proposed. The so called, optimal disturbances, widely used in the aerodynamic stability theory for mathematical models without delays are constructed for pert...

The problem of asymmetric incompressible axial flow in a corner formed of two intersecting plates at a right angle is considered. The asymptotic behaviour of the flow far away from the corner is analysed. Two types of asymptotic behaviour are found. It is shown that the flow is very sensitive to the asymmetry parameter. A comparison of the results...

This work is devoted to computations of invariant pairs associated with separated groups of finite eigenvalues of large regular non-linear matrix pencils. It is proposed to combine the method of successive linear problems with a Newton-type method designed for partial linear eigenproblems and a deflation procedure. This combination is illustrated w...

A combined theoretical and numerical analysis of an experiment devoted to the excitation of Görtler vortices by localized stationary or vibrating surface nonuniformities in a boundary layer over a concave surface is performed. A numerical model of generation of small-amplitude disturbances and their downstream propagation based on parabolic equatio...

Evolution equations of small disturbances aimed to compute the location of a laminar–turbulent transition in boundary layers by the eN-method taking into account the compressibility and heat transfer are described and justified for aerodynamic applications. The results of computation of N-factors and transition locations with the use of locally-par...

This work is devoted to finding maxima of the function where and is a large sparse matrix whose eigenvalues have negative real parts but whose numerical range includes points with positive real parts. Four methods for computing are considered which all use a special Lanczos method applied to the matrix and exploit the sparseness of through matrix-v...

This work is devoted to computations of deflating subspaces associated with separated groups of finite eigenvalues near specified shifts of large regular matrix pencils. The proposed method is a combination of inexact inverse subspace iteration and Newton’s method. The first one is slow but reliably convergent starting with almost an arbitrary init...

The stability of Poiseuille flow in channels with walls grooved in the streamwise direction is investigated numerically. In the framework of physically justified scaling of velocity and length, an analysis of energy and linear critical Reynolds numbers was carried out in a practically important range of groove heights, sharpness and spacing. It is...

Efficient inverse subspace bi-iteration and bi-Newton methods for computing the spectral projector associated with a group of eigenvalues near a specified shift of a large sparse matrix is proposed and justified. Numerical experiments with a discrete analogue of a non-Hermitian elliptic operator are discussed to illustrate the theory.

An original technology of stability analysis of an airfoil boundary layer is presented in this paper. The technology includes an extraction of the boundary layer from the results of laminar flow computations, the computation of neutral curves and increments of Tollmien-Schlichting waves, and the computation of the location of laminar-turbulent tran...

The present paper is devoted to the Hermitian spectral pseudoinversion and its applications to analysis, the solution and reduction of Hermitian differential-algebraic systems. New explicit formulas for the solutions of such systems and the solutions of related generalized Lyapunov equations are proposed. Attainable upper bounds for the norms of th...

A new effective method for solving Hermitian differential–algebraic systems with constant coefficients is proposed and justified. It uses an explicit representation of the solution based on the spectral pseudo-inversion and an expansion of the matrix exponential via Laguerre polynomial series. An approximate solution is obtained by truncating the s...

The present work is devoted to a description and substantiation of an original module for computing the location of laminar-turbulent transition in subsonic boundary layer flows, which is based on the eN -method and enables more accurate computations of the flow around bodies in the presence of the so-called natural transition to turbulence in the...

This work is focused on the computation of the invariant subspace associated with a separated group of eigenvalues near a specified shift of a large sparse matrix. First, we consider the inverse subspace iteration with the preconditioned GMRES method. It guarantees a convergence to the desired invariant subspace but the rate of convergence is at be...

A laminar flow of a viscous incompressible fluid with a constant pressure gradient (Poiseuille flow) is considered in a rectangular duct for different values of cross-sectional aspect ratio. A new method, significantly more efficient than the known ones, is proposed and justified for computing the critical Reynolds number of such a flow. The depend...

A new generalized inversion for square matrices based on projections is introduced. It includes as special cases known generalized inverses such as the Moore-Penrose and the Drazin inverses. When associated with a regular matrix pencil, it can be expressed by a contour integral formula and can be used, in particular, to write down an explicit repre...

An excitation and growth of nonstationary Görtler vortices of different frequencies and spanwise wavenumbers in a Blasius like boundary layer over a concave wall was studied experimentally only recently. In-depth analysis of the experimental data provided detailed databases on both the generation of the control flow disturbances due to surface vibr...

We describe an effective approach for computing the maximum amplification of the solution norm of linear differential-algebraic systems that arise, in particular, when approximating with respect to space variables the linearized viscous incompressible flow equations for disturbances of laminar flows. In this context the square of the maximum amplif...

Dependence of the linear stability of Poiseuille flows in a rectangular duct on the cross-sectional aspect ratio is studied. Steady laminar viscous incompressible flow with a fix pressure, the velocity vector, and the velocity distribution satisfying the Poisson equation, is considered. The analysis of the linear stability of the Poiseuille flow is...

This work is devoted to computing the function γ(t) = ∥ exp(tA)∥2 in a given time interval 0 ≤ t1 ≤ t ≤ t2, where A is a square matrix whose eigenvalues have negative real parts. The main emphasis is put on computations of the maximal value of γ(t) for t ≥ 0. To speed up the computations, we propose and justify a new algorithm based on low-rank app...

This work is devoted to the numerical analysis of small flow disturbances, i.e. velocity and pressure deviations from the steady state, in ducts of constant cross sections. The main emphasis is put on the disturbances causing the most kinetic energy density growth, the so-called optimal disturbances, whose knowledge is important in laminar-turbulen...

The study is devoted to formulation, substantiation and numerical solution of problems related to temporal stability of laminar flows of viscous incompressible fluid in plane channels with grooved walls. Shapes of the grooves resembling riblets used in practice are considered. An innovative technique of dimension reduction of the linearized Navier-...

We discuss two constructive approaches to the solution of problems of polynomial approximation in the uniform (Chebyshev) norm and also attainable estimates of the solution norms for initial value problems for Hermitian systems of differential and algebraic equations.

Problems related to the temporal stability of laminar viscous incompressible flows in plane channels with ribbed walls are formulated, justified, and numerically solved. A new method is proposed whereby the systems of ordinary differential and algebraic equations obtained after a spatial approximation are transformed into systems of ordinary differ...

We propose and justify an upper bound for voltage settling time in RC-circuits based on a new upper bound for the solution norm of Hermitian ODAE systems. An algorithm for efficient calculation of this upper bound is proposed. Results of numerical experiments are presented and discussed.