Papers by Evgenii Vorozhtsov
On some methods for the numerical simulation of flows with complex structure
Computer Methods in Applied Mechanics and Engineering, Mar 1, 1979
ABSTRACT This paper represents a survey of the investigation carried out at the Institute of Theo... more ABSTRACT This paper represents a survey of the investigation carried out at the Institute of Theoretical & Applied Mechanics of the Siberian Division of the USSR Academy of Sciences. The questions of construction of efficient difference schemes are considered for the numerical integration of a compressible viscous heat-conducting gas based on splitting in terms of the physical processes and the space variables in conjunction with adaptation to difference grids that move with the flow. The questions of the interpretation of the shock-capturing computational results of the gas-dynamical problem solution are also considered, in particular the problem of shock wave localization in the numerical simulation of flows of an inviscid, no-heat-conducting, compressible gas. The methods presented are especially efficient in computations of flows with complex structure where singular zones and elements are present (e.g. shock waves and transitions, contact stripes, boundary layers, double and triple shock configurations etc.).
Differential Analyzers of Shock Waves in Two-Dimensional Gas Dynamic Computations
On the property of difference schemes of gas dynamics—II
Computers & Fluids, 1982
ABSTRACT
Smoothed Particle Hydrodynamics Method Used for Numerical Simulation of Impact Between an Aluminum Particle and a Titanium Target
Journal of Applied Mechanics and Technical Physics, Dec 1, 2022
The property of K-consistency for difference schemes of gas dynamics
Akademiia Nauk SSSR Doklady, 1981
It is demonstrated that the property of K-consistency can be determined directly for finite diffe... more It is demonstrated that the property of K-consistency can be determined directly for finite difference schemes that approximate the Euler equations of gas dynamics. Algorithms for the suppression of K-nonconsistency in the use of schemes of first and second orders of accuracy are validated.
Ordinary differential equations with the aid of lagrange-burmann expansions
Computer Algebra in Scientific Computing, Sep 6, 2010
Higher-order symplectic integration techniques for molecular dynamics problems
Journal of Computational Physics, Mar 1, 2022
On the property of difference schemes of gas dynamics—I
Computers & Fluids, 1982
ABSTRACT The notion of of the first differential approximation of a difference scheme is one of t... more ABSTRACT The notion of of the first differential approximation of a difference scheme is one of the basic notions of a one-dimensional theory of a contact strip developed recently by the authors. In the present paper it is shown that it is possible to introduce the notion directly for finite difference shock-capturing schemes approximating the Euler equation system for an inviscid, compressible gas. Methods for increasing the accuracy of the numerical solutions in the vicinity of a contact discontinuity are proposed and theoretically justified. These methods apply to the cases when the equation of state employed does not satisfy the condition. Theoretical conclusions are illustrated by computational examples.
On some methods for the numerical simulation of flows with complex structure
Springer eBooks, Apr 6, 2008
ABSTRACT This paper represents a survey of the investigation carried out at the Institute of Theo... more ABSTRACT This paper represents a survey of the investigation carried out at the Institute of Theoretical & Applied Mechanics of the Siberian Division of the USSR Academy of Sciences. The questions of construction of efficient difference schemes are considered for the numerical integration of a compressible viscous heat-conducting gas based on splitting in terms of the physical processes and the space variables in conjunction with adaptation to difference grids that move with the flow. The questions of the interpretation of the shock-capturing computational results of the gas-dynamical problem solution are also considered, in particular the problem of shock wave localization in the numerical simulation of flows of an inviscid, no-heat-conducting, compressible gas. The methods presented are especially efficient in computations of flows with complex structure where singular zones and elements are present (e.g. shock waves and transitions, contact stripes, boundary layers, double and triple shock configurations etc.).
Optimization Techniques of the Discontinuities Localization
Differential Analyzers of Shock Waves in One-Dimensional Gas Flows
Springer eBooks, 1990
Difference Solution Refinement in the Neighborhood of Strong Discontinuities
Springer eBooks, 1990
Introduction and Necessary Notions from the Theory of Difference Schemes for Gas Dynamics Problems
A Search Method for the Construction of Maximally Stable Difference Schemes for Partial Differential Equations
Springer eBooks, 1987
Journal of Symbolic Computation, Sep 1, 1999
The paper deals with problems arising in the application of the computer algebra systems for the ... more The paper deals with problems arising in the application of the computer algebra systems for the symbolic-numeric stability analysis of difference schemes and schemes of the finite-volume method approximating the two-dimensional Euler equations for compressible fluid flows on curvilinear spatial grids. We carry out a detailed comparison of the REDUCE 3.6 and Mathematica (Versions 2.2 and 3.0) from the point of view of their applicability to the solution of the above problems. We draw a conclusion that a preference should be given for Mathematica from the viewpoint of the execution of symbolic-numeric computations. We also describe in detail our new symbolic-numeric algorithm for stability investigation, which was implemented with the aid of Mathematica. The proposed method enables us to reduce the needed computer storage at the symbolic stages by a factor of about 20 as compared with the previous algorithms. A feature of the numerical stages is the use of the arithmetic of rational numbers, which enables us to avoid the accumulation of the roundoff errors. We present the examples of the application of the proposed symbolic-numeric method for stability analysis of very complex schemes of the finite-volume method on curvilinear grids, which are widely used in computational fluid dynamics.
Solution to the problems of gas movement in coal seams with nonlinear filtration laws
Soviet mining science, 1978
ABSTRACT
Digital Diagnostics of Multiphase Flows by the Pattern Recognition Techniques
NASA STI/Recon Technical Report N, Jul 1, 2002
ABSTRACT It should be noted that the methods of digital patten recognition were applied only for ... more ABSTRACT It should be noted that the methods of digital patten recognition were applied only for the diagnostics of pure gas flows. At the same time, as is known from the theory of two-phase flows of the mixtures of gas and solid particles, the shock waves as well as of other singularities can arise in such flows, and the number of different types of singularities in two-phase flows even proved to be larger than in the case of pure gas flows. A generalization of the algorithms for digital localization and classification of singularities described is proposed in the present work for the case of two-phase flows of the mixtures of gas and solid particles. The examples of the diagnostics of specific flows are presented.
Stability Analysis of Nonlinear Difference Schemes
GROOME - Tool Supported Graphical Object Oriented Modelling for Computer Algebra and Scientific Computing
Springer eBooks, 2001
ABSTRACT
Applied Mathematics and Computation, Dec 1, 2019
The preconditioner, multigrid algorithm, and the Krylov method are applied for accelerating the i... more The preconditioner, multigrid algorithm, and the Krylov method are applied for accelerating the iteration process of solving the Navier-Stokes equations by the method of collocations and least residuals (CLR). These methods have been used simultaneously in their combination and separately. Their capabilities and efficiency have been verified by a considerable number of numerical experiments. To find the parameters of a preconditioner proposed in the work a relatively simple problem of minimizing the condition number of the system of linear algebraic equations to the solution of which the solution of the Navier-Stokes equation is reduced is solved. The original criterion of the degeneration degree of the Krylov subspace basis enables an automatic reduction of the subspace basis without a computer code restart in the region of small residuals of the PDE solution thereby improving the stability of iteration process in the above region. A combined simultaneous application of all three techniques for accelerating the iterative process of solving the boundary-value problems for two-dimensional Navier-Stokes equations has reduced the CPU time of their solution on computer by the factors up to 160 as compared to the case when none of them was applied. The proposed combination of the techniques for speeding up the iteration processes may be implemented also at the use of other numerical methods for solving the PDEs.
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Papers by Evgenii Vorozhtsov