# Vladimir A. TitarevFederal Researcher Center "Computer Science and Control" of Russian academy of sciences · Mechanics

Vladimir A. Titarev

Ph.D.

Adding the Rykov kinetic model to my Nesvetay code

## About

119

Publications

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3,912

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Citations since 2016

Introduction

I am interested in computational fluid dynamics and associated numerical analysis as well as parallel computing.

Additional affiliations

October 2011 - present

March 2007 - March 2011

November 2005 - March 2007

## Publications

Publications (119)

We propose a direct arbitrary Lagrangian-Eulerian (ALE) variant of the previously developed discrete velocity method to solve the kinetic equation with the Bhatnagar–Gross–Krook (BGK) model collision integral. The effectiveness and robustness of the new scheme are demonstrated by computing the axisymmetric plume expansion into a low pressure gas du...

A numerical study in a one-dimensional planar formulation of the dynamics of the neutral gas expansion during nanosecond laser evaporation into a low-pressure background gas is carried out using two different kinetic approaches: the direct simulation Monte Carlo method and direct numerical solution of the Bhatnagar–Gross–Krook equation. Results wer...

Complex systems have long been an integral part of modern life and can be encountered everywhere [...]

UCNS3D is an open-source computational solver for compressible flows on unstructured meshes. State-of-the-art high-order methods and their associated benefits can now be implemented for industrial-scale CFD problems due to the flexibility and highly-automated generation offered by unstructured meshes. We present the governing equations of the physi...

The article considers the problem of optimizing (from the viewpoint of soundproofing capacity) the framework of a reinforced shell under the action of the propeller’s acoustic field. Nonstationary data and the pressure field from the propeller on the surface were obtained using a software package that implements an implicit numerical method with a...

A numerical study of the planar gas expansion under pulsed evaporation into the background gas is carried out. The chosen conditions are typical for nanosecond laser deposition of thin films and nanostructure synthesis, with the saturated gas pressure at the surface of 5.4 MPa and the background pressure of 50 and 500 Pa. The problem is solved base...

The paper presents a new solver for the numerical solution of the Boltzmann kinetic equation with the Shakhov model collision integral (S-model) for arbitrary spatial domains. The numerical method utilizes the Tucker decomposition, which reduces the required computer memory for up to 100 times, even on a moderate velocity grid. This improvement is...

The numerical study of one-dimensional gas expansion under pulsed evaporation into vacuum is carried out on the basis of the direct simulation Monte Carlo method, the exact Boltzmann kinetic equation, and the S-model kinetic equation. The results are presented for various levels of evaporation intensity, defined by the amount of evaporated material...

For modeling turbulent flow, the near-wall domain decomposition (NDD) approach initially proposed by the second author and recently developed in a number of papers proved to be very efficient. It leads to a non-overlapping domain decomposition with a Robin-to-Dirichlet map between an inner (near-wall) and outer regions. The regions are linked with...

The paper is a short review of the recent results of the author in the development of numerical methods and parallel computer code Nesvetay to solve kinetic equations with approximate (model) collision integrals. The efficiency and robustness of the methods are demonstrated by computing \(M_\infty =25\) rarefied gas flow over a model winged geometr...

In near-wall turbulence modeling it is necessary to resolve a thin boundary layer containing high gradients of the solution. An accurate enough resolution of such a layer can take most of the computational time. The situation becomes even worse for unsteady problems. To avoid time-consuming computations, in the present paper a new approach is devel...

The study of nonstationary rarefied gas flows is currently paid much attention. Such interest to these problems is caused by the creation of pulsed jets used for the deposition of thin films and special coatings on solid surfaces. However the problems of nonstationary rarefied gas flows have not been studied sufficiently fully because of their larg...

Paper presents a new solver for numerical solution of the Boltzmann kinetic equation with Shakhov model collision integral (S-model) for arbitrary spatial domains. Numerical method utilizes Tensor-Train decomposition, which allows to reduce required computer memory for up to 30 times even on a moderate velocity mesh. This improvement is achieved by...

The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years, including both methodological aspects as well as very ambitious applications. In spite of methodological progress, the issues of efficiency and ease of implementation of the solution of the associated generalized Rie...

The paper is devoted to the comparative study of Shakhov model kinetic equation and Direct Simulation Monte Carlo (DSMC) solutions as applied to high-speed flow of a monatomic gas over generic three-dimensional space vehicle under angle of attack. The corresponding calculations are carried out using Nesvetay and SMILE software packages, developed b...

The unsteady two-dimensional problem of the reflection of a uniform supersonic rarefied-gas flow incident normal on a wall with an orifice and the gas outflow through the orifice (slot or channel) is solved on the basis of the kinetic S-model. The slot influence on the reflection nature, the velocity of the shock wave reflected from the wall, and t...

Resolution of a near-wall boundary layer is one of hot topics in turbulence modeling. It often requires most of computational time. A non-overlapping domain decomposition method has turned out to be very efficient to tackle this problem for engineering applications. The method is much more universal than conventional approaches based on wall functi...

We study axisymmetric time-dependent problem of reflection of a shock wave running into the wall with a short orifice and associated rarefied gas flow into vacuum through a pipe. The main characteristics under consideration are the mass flow rate through the pipe and its transition to the constant value, the influence of the orifice presence, pipe...

The development of the software package FlowModellium designed for simulating high-speed flows of continuum medium taking into account nonequilibrium chemical reactions is described. The numerical method and the two-level parallel algorithm used in the package are presented. Examples of computations are discussed.

The influence of the position of the pylon on the characteristics of propeller noise has been studied as applied to environmental noise calculations for future aircraft. Components related to propeller noise itself and to a signal reflected from a pylon have been separated in the overall noise produced by the propeller–pylon system at the blade pas...

The study of non-stationary rarefied gas flows is, currently, attracting a great deal of attention. Such an interest arises from creating the pulsed jets used for deposition of thin films and special coatings on the solid surfaces. However, the problems of non-stationary rarefied gas flows are still understudied because of their large computational...

Numerical solution of the Boltzmann equation for stationary high-speed flows around complex three-dimensional bodies is an extremely difficult computational problem. This is because of high dimension of the equation and lack of efficient implicit methods for the calculation of the collision integral on arbitrary non-uniform velocity grids. Therefor...

For the purpose of taking the internal degrees of freedom into account, threetemperature approximating model equations, which are a generalization of the R- and ES–BGKmodels, are proposed for a diatomic gas. The surface pressure, friction, and heat transfer coefficients are compared with the direct simulation Monte Carlo (DSMC) solution in the prob...

This special issue is dedicated to recent developments concerning modern numerical methods for time dependent partial differential equations that can be used to simulate complex nonlinear flow and transport processes and tries to cover a wide spectrum of different applications and numerical approaches.
Most of the models under consideration here ar...

Different parallel distributed-memory versions of Lower-Upper Symmetric Gauss–Seidel (LU-SGS) method for solution of discrete equations in finite-volume framework are compared in terms of parallel structure of algorithms. New version based on multilevel recursive decomposition is proposed.

The two-dimensional time-dependent problem of rarefied gas flow in a plane channel, formed by parallel plates of finite length and closed at one end, is solved on the basis of the kinetic S-model. The flow develops as a result of rupture of a diaphragm which separates the gas at rest in the channel and the gas at rest in a reservoir of infinite vol...

A new parallel version of the method LU-SGS (Lower-upper symmetric Gauss-Seidel) based on a multilevel decomposition of the unstructured computational mesh is proposed. The advantages of the proposed approach are demonstrated by computing the supersonic flow around the RAM-C geometry. The method is well scalable when a large number of threads are u...

The paper is devoted to the further development of the numerical methods to solve model kinetic equations and their application to hypersonic rarefied gas flows. Firstly, we verify the accuracy of the approach by comparing our results with the well resolved DMSC calculations for argon and nitrogen. Secondly, computation of an external flow over a m...

The paper is devoted to the development of the numerical approaches to solve model kinetic equations as applied to computing high-speed rarefied gas flows over three-dimensional geometries. The use of a very non-uniform unstructured velocity mesh is proposed, and the influence of the velocity mesh resolution is studied in detail. The test problems...

The range of validity of various linear kinetic modelling approaches simulating rarefied pressure driven gas flow through circular tubes is computationally investigated by comparing the flowrates obtained by the linear approaches with the corresponding nonlinear ones. The applicability margins of the linear theories in terms of the parameters deter...

A two-level OpenMP + MPI parallel implementation is used to numerically solve a model kinetic equation for problems with complex three-dimensional geometry. The scalability and robustness of the method are demonstrated by computing the classical gas flow through a circular pipe of finite length and the flow past a reentry vehicle model. It is shown...

The kinetic S-model is used to study the unsteady rarefied gas flow through a plane channel between two parallel infinite plates. Initially, the gas is at rest and is separated by the plane x = 0 with different pressure values on opposite sides. The gas deceleration effect of the channel walls is studied depending on the degree of gas rarefaction a...

The time-dependent problem of the development of a rarefied flow in a plane channel formed by two parallel infinite plates is considered on the basis of a kinetic model. At the initial moment of time the gas at rest occupies half the channel and borders on a vacuum. The effect of gas deceleration at the channel walls is studied as a function of the...

The paper is devoted to the analysis of the time-dependent rarefied gas flow into vacuum from a circular pipe closed at one end. The problem is studied numerically on the basis of the S-model kinetic equation up to an very large output time. The results demonstrate the dependence of flow pattern and evacuation time on the Knudsen number and pipe&ap...

The paper is devoted to the study of a rarefied gas flow through a composite circular pipe into vacuum. The pipe is made of two cylindrical sections of different diameters. Two cases are studied: wider pipe followed by narrower pipe (converging configuration) and the narrower pipe followed by the wider (diverging configuration). The analysis is bas...

The paper is devoted to the analysis of the time-dependent rarefied gas flow into vacuum from a circular pipe closed at one end. The problem is studied numerically on the basis of the S-model kinetic equation. Limiting solutions corresponding to the one-dimensional free-molecular and hydrodynamic flow regimes are also considered. The results demons...

Analysis of three-dimensional rarefied gas flowsin microdevices (micropipes, micropumps etc) and over re-entry vehicles requires development of methods of computational modelling. One of such methods is the direct numerical solution of the Boltzmann kinetic equation for the velocity distribution function with either exact or approximate (model) col...

The problem of rarefied gas flow into vacuum through a short circular pipe is studied numerically by solving the Boltzmann kinetic equation. Comparison of the results obtained with the exact and S-model collision integrals is presented across a large range of Knudsen numbers. Computed values of mass flow rate are also compared against the DSMC resu...

The paper is devoted to the study of a rarefied gas flow through a finite length conical pipe into vacuum. The problem is solved in the complete geometrical setup, which included not only the pipe, but also high- and low-pressure reservoirs. The analysis is based on the direct numerical solution of the Boltzmann kinetic equation with the S-model co...

The paper is devoted to the further development and systematic
performance evaluation of a recent deterministic framework Nesvetay-3D
for modelling three-dimensional rarefied gas flows. Firstly, a review of
the existing discretization and parallelization strategies for solving
numerically the Boltzmann kinetic equation with various model collision...

The problem of steady outflow of rarefied gas from a reservoir into vacuum through a long cylindrical tube of circular cross-section at a constant temperature is considered on the basis of the kinetic S-model. The kinetic equation is solved numerically using a conservative second-order method. The basic calculated quantity is the gas flow rate thro...

The paper is devoted to the study of a rarefied gas flow through a circular pipe caused by small pressure differences between the reservoirs attached to the ends of the pipe. The analysis is based on of the direct numerical solution of the Boltzmann kinetic equation with the linearized model collision integral of Shakhov. The solution of the proble...

The kinetic S-model is used to study the steady rarefied gas flow
through a long pipe of variable cross section joining two tanks with
arbitrary differences in pressure and temperature. The kinetic equation
is solved numerically by applying a second-order accurate conservative
method on an unstructured mesh. The basic quantity to be computed is the...

A parallel multiblock implementation of a second-order accurate implicit numerical method based on solving a model kinetic equation is proposed for analyzing three-dimensional rarefied gas flows. The performance of the method is illustrated by computing test examples of gas flows in a circular pipe in a wide range of Knudsen numbers. The convergenc...

Rarefied gas flow through a circular pipe into vacuum is studied on the
basis of the direct numerical solution of the kinetic equation. The main
emphasis of the study is on the end effects. The problem is solved in
the completed geometrical setup with the pipe and reservoirs as well as
incomplete setup in which the reservoirs are replaced by emissi...

The linearized kinetic S-model is used to study the non-isothermal
steady rarefied gas flow driven by differences in pressure and
temperature in a plane channel between long finite parallel plates
joining two reservoirs of infinite volume. An efficient composite
(asymptotic) method is developed: a one-dimensional asymptotic solution
corresponding t...

Flow of diatomic rarefied gas in capillary of infinite length with
circular cross section caused by small pressure gradient (Poiseuille
flow) and/or small temperature gradient (thermal creep flow) is studied
numerically on the basis of kinetic model taking into account rotational
degrees of freedom of molecule (R-model). The main quantity calculate...

The hypersonic rarefied gas flow over blunt bodies in the transitional
flow regime, typical of the reentry flight of space vehicles at
altitudes higher 90-100 km, is investigated. As an example, the problem
of hypersonic flows over long blunt wings and axisymmetric bodies is
considered. It is analyzed in a wide range of the free stream Knudsen
numb...

The paper is devoted to the further development of a recent
deterministic framework Nesvetay-3D for modelling of three-dimensional
rarefied gas flows on the basis of the numerical solution of the
Boltzmann kinetic equation with various model collision integrals.
Performance of the framework is demonstrated on a gas flow in long
finite-length circul...

The paper presents a numerical analysis of the nonlinear rarefied gas flow through a long planar channel of finite length. The solution is constructed for the arbitrary pressure and temperature drops, including flow into vacuum. The obtained results for the flow rates are compared with the linearized solutions in the large range of degree of gas ra...

Flow of a diatomic rarefied gas in a capillary tube of infinite length and an arbitrary cross-section under a given small pressure gradient (Poiseuille flow) or a small temperature gradient (thermal creep) is studied on the basis of a kinetic model that takes account for the rotational degrees of freedom of molecules (R-model). Numerical investigat...

The paper is devoted to the development of an efficient deterministic frame-work for modelling of three-dimensional rarefied gas flows on the basis of the numer-ical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshe...

The paper presents an analysis of the non-linear rarefied gas flow through a circular pipe into vacuum. The main attention is given to the case of the large length to radius ratio. The problem is studied on the basis of the numerical solution of the S-model kinetic equation. Results are compared with the available DSMC data for short tubes as well...

The linearized kinetic S-model is used to study the nonisothermal steady rarefied gas flow driven by differences in pressure and temperature in a plane channel between long finite parallel plates joining two tanks of infinite volume. An efficient composite (asymptotic) method is developed: a one-dimensional asymptotic solution corresponding to an i...

An efficient numerical algorithm for calculating rarefied gas flows in planar microchannels on the basis of the Boltzmann kinetic equation with the linearized S-model collision integral is presented. The algorithm consists of a high-order spatial discretisation on unstructured meshes, conservative procedure to calculate macroscopic quantities and e...

The paper presents a linear high-order method for advection–diffusion conservation laws on three-dimensional mixed-element unstructured meshes. The key ingredient of the method is a reconstruction procedure in local computational coordinates. Numerical results illustrate the convergence rates for the linear equation and a non-linear hyperbolic syst...

An isothermal steady rarefied gas flow in a long channel (tube) of elliptical or rectangular cross-section under the action
of a given pressure gradient (Poiseuille flow) is studied on the basis of the Bhatnagar-Gross-Krook model. The solution is
obtained using a conservative higher-order method. The velocity field in a channel cross-section is inv...

The paper extends weighted essentially non-oscillatory (WENO) methods to three dimensional mixed-element unstructured meshes, comprising tetrahedral, hexahedral, prismatic and pyramidal elements. Numerical results illustrate the convergence rates and non-oscillatory properties of the schemes for various smooth and discontinuous solutions test cases...

The nonisothermal steady rarefied gas flow driven by a given pressure gradient (Poiseuille flow) or a temperature gradient
(thermal creep) in a long channel (pipe) of an arbitrary cross section is studied on the basis of the linearized kinetic S-model. The solution is constructed using a high-order accurate conservative method. The numerical comput...

The method based on the numerical solution of a model kinetic equation is proposed for analyzing three-dimensional rarefied
gas flows. The basic idea behind the method is the use of a second-order accurate TVD scheme on hybrid unstructured meshes
in physical space and a fast implicit time discretization method without iterations at the upper level....

The paper extends weighted essentially non-oscillatory (WENO) schemes to two-dimensional quadrilateral and mixed-element unstructured meshes. The key element of the proposed methods is a reconstruction procedure suitable for arbitrarily-shaped cells. The resulting schemes achieve the designed uniformly high-order of accuracy and compute discontinuo...

An implicit high-order accurate method for solving model kinetic equations is proposed. The method is an extension of earlier work on the construction of an explicit TVD method for hybrid unstructured meshes in physical space and is illustrated on the Poiseuille flow of rarefied gas. Examples of calculations are provided for different Knudsen numbe...

The linearized kinetic BGK model is used to study the steady Poiseuille flow of a rarefied gas in a long channel of rectangular
cross section. The solution is constructed using the finite-volume method based on a TVD scheme. The basic computed characteristic
is the mass flow rate through the channel. The effect of the relative width of the cross se...

A high-order accurate method is proposed for analyzing the isothermal rarefied gas flow in an infinitely long channel with
an arbitrarily shaped cross section (Poiseuille flow). The basic idea behind the method is the use of hybrid unstructured
meshes in physical space and the application of a conservative technique for computing the gas velocity....

The paper presents preliminary computational results of surface ablation around double-cone flare geometry. The analysis is based on Park's ablation model, which is fully coupled with the non-equilibrium real gas flow model. The equations are solved using second-order high-resolution methods implemented into the in-house code CNS3D. Comparisons of...

Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based up...

A high-order accurate method for analyzing two-dimensional rarefied gas flows is proposed on the basis of a nonstationary
kinetic equation in arbitrarily shaped regions. The basic idea behind the method is the use of hybrid unstructured meshes
in physical space. Special attention is given to the performance of the method in a wide range of Knudsen...

The flow around the ONERA RA16SC1 three-element airfoil was numerically investigated using three different computational strategies: the Unsteady Reynolds-Averaged Navier-Stokes Equations (URANS), the Detached Eddy Simulation (DES) and the Implicit Large Eddy Simulation (ILES). Two different numerical schemes were employed: the Jameson's Central Di...

The kinetic equation for a monatomic gas with a model collision operator (S-model) is used to study the development and tending to steady state of one-dimensional unsteady half-space gas condensation
on a plane condensed phase. Initially, the gas is at rest and in equilibrium with the body’s surface and, then, the body temperature
suddenly drops to...

The time-dependent one-dimensional problem of the normal reflection of a shock wave propagating at constant velocity in a gas (vapor) at rest from the plane surface of its condensed phase under steady-state condensation-evaporation conditions on the interphase plane is considered within the framework of the kinetic equation for a monatomic gas with...

We study the cylindrical Couette flow of a rarefied gas between two cylinders in the generalized setup in which the inner of which not only rotates but also slides along its axis. The analysis is based on the numerical solution of the S-model kinetic equation. The influence of ratio of cylinder radiuses, velocities of the inner cylinder and Knudsen...

The present work is devoted to the computational modelling of the process of beam action on a lithium target. The aim of the investigation is to determine the maximum values of temperature and pressure as well as general pattern of the process. The analysis is based on the compressible Euler equations with the stiffened gas equation of state with p...

The structure of a normal (direct) shock in a gas for the parameters corresponding to nitrogen is investigated with allowance for the rotational degrees of freedom on the basis of a model kinetic equation. For various Mach numbers the structure is compared with both the known experimental results and the solutions of the Navier-Stokes approximation...

In this paper we present the exact solution of the Riemann problem for the non-linear shallow water equations with a step-like bottom. The solution has been obtained by solving an enlarged system that includes an additional equation for the bottom geometry and then using the principles of conservation of mass and momentum across the step. The resul...

The present paper is devoted to the construction and comparative study of upwind methods as applied to the system of one-dimensional non-linear elasticity equations with particular attention to robustness and accurate resolution of delicate features such as linearly degenerate fields. Copyright © 2007 John Wiley & Sons, Ltd.

This paper deals with the construction of high-order ADER numerical schemes for solving the one-dimensional shallow water equations with variable bed elevation. The non-linear version of the schemes is based on ENO reconstructions. The governing equations are expressed in terms of total water height, instead of total water depth, and discharge. The...

ADER is a recent Godunov-type approach for constructing arbitrarily highorder finite-volume schemes for hyperbolic conservation
laws. The idea was first proposed for the constant coefficient linear advection equation in multiple space dimensions [12].
The extension to nonlinear systems is based on the approximate solution procedure for the so-calle...

A new conservative discrete ordinate method for nonlinear model kinetic equations is proposed. The conservation property with respect to the collision integral is achieved by satisfying at the discrete level approximation conditions used in deriving the model collision integrals. Additionally to the conservation property, the method ensures the cor...

In this article we present a quadrature-free essentially non-oscillatory finite volume scheme of arbitrary high order of accuracy both in space and time for solving nonlinear hyperbolic systems on unstructured meshes in two and three space dimensions. For high order spatial discretization, a WENO reconstruction technique provides the reconstruction...

The two-dimensional supersonic rarefied gas flow past an infinite plate placed normally to the flow is analyzed. The gas possesses rotational degrees of freedom. The problem is stated for a model kinetic equation and is solved by applying a second-order accurate implicit conservative finite-difference method. The gas parameters correspond to nitrog...

We study stability properties and truncation errors of the finite-volume ADER schemes on structured meshes as applied to the
linear advection equation with constant coefficients in one-, two- and three-spatial dimensions. Stability of linear ADER
schemes is analysed by means of the von Neumann method. For nonlinear schemes, we deduce the stability...

This paper is about numerical fluxes for hyperbolic systems and we first present a numerical flux, called GFORCE, that is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first-order upwind method. Then we incorporat...

An implicit quasi-monotone second-order accurate method is proposed for analyzing the spiral Couette flow of a rarefied gas
between coaxial cylinders. The basic advantages of the method over the conventional method of stationry iterations are that
the former is conservative with respect to the collision integral, has a simple software implementatio...

In this paper, we first briefly review the semi-analytical method [E.F. Toro, V.A. Titarev, Solution of the generalized Riemann problem for advection–reaction equations, Proc. Roy. Soc. London 458 (2018) (2002) 271–281] for solving the derivative Riemann problem for systems of hyperbolic conservation laws with source terms. Next, we generalize it t...