Papers by Evgenii Vorozhtsov
Modern Birkhäuser classics, 2017
Computers & Fluids, Mar 1, 1981
ABSTRACT
We present a new symbolic-numerical method for an automatic stability analysis of difference sche... more We present a new symbolic-numerical method for an automatic stability analysis of difference schemes approximating scalar linear or nonlinear partial differential equations (PDEs) of hyperbolic or parabolic type. In this method the grid values of the numerical solution for any fixed moment of time are considered aa random correlated variables obeying the normal distribution law. Therefore, one can apply the notion of the Shannon's entropy to characterize the stability of a difference scheme. The reduction of this entropy, or uncertainty, is taken as a stability criterion. It is shown at a number of examples that this criterion yields the same stability regions in the cases of linear difference initialvalue problems, as the Fourier method. In the case of two spatial variables the present probabilistic method is computationally by two orders of magnitude faster than the Fourier method. *At the moment GH-Univemity of the Kassel, FB -17 Mathematik, Hollaendische str. 36,
Akademiia Nauk SSSR Doklady, Mar 1, 1976
ABSTRACT
The Navier-Stokes equations governing the three-dimensional flows of a viscous, compressible, hea... more The Navier-Stokes equations governing the three-dimensional flows of a viscous, compressible, heat-conducting gas and augmented by turbulence modeling present the most realistic model for gas flows around the elements of aircraft configurations. We study the stability of one of the Jameson's schemes of 1981, which approximates the set of five Navier-Stokes equations completed by the turbulence model of Baldwin and Lomax. The analysis procedure implements the check-up of the necessary von Neumann stabtity criterion. It is shown with the aid of the proposed symbolicnumeric strategy that the physical viscosity terms in the Navier-Stokes equations have a dominant effect on the sizes of the stability region in comparison with the heat conduction terms. It turns out that the consideration of turbulence wit h the aid of eddy viscosity model of Baldwin and Lomax has an insignificant effect on the size of the necessary stabilit y region.
Computers & Fluids, Mar 1, 1981
ABSTRACT
The matrix H is also called the stability matrix (Gilmore 1981). Definition 4.1. The points K € ?... more The matrix H is also called the stability matrix (Gilmore 1981). Definition 4.1. The points K € ? a t which W = 0 are called the critical points of the smooth function V(K, £ ) . Definition 4.2. The critical points at which det H \£ 0 are called isolated, nondegenerate, or Morse critical points. Definition 4.3. The critical points of the function V(K, £) at which det H = 0 are called nonisolated, degenerate, or non-Morse critical points. Consider a smooth coordinate change (i.e., having the derivatives of any order)
Vyčislitelʹnye metody i programmirovanie, Jan 20, 2019
Предложена и реализована p-версия метода коллокации численного решения интегральных уравнений Фре... more Предложена и реализована p-версия метода коллокации численного решения интегральных уравнений Фредгольма второго рода. В данной реализации осуществлены возможности варьирования степени полинома в полиномиальном представлении приближенного решения уравнений и варьирования количества узлов используемой квадратурной формулы Гаусса для влияния на точность решения. Исследовано влияние числа точек коллокации, использованных для аппроксимации решения, и количества узлов квадратурной формулы Гаусса на число обусловленности системы линейных алгебраических уравнений, к решению которой сводится построение приближенного решения, и на его точность путем численного решения примеров, в том числе приведенных в известных изданиях. Предложенный алгоритм реализован на языке программного пакета Mathematica. Во всех рассмотренных примерах предложенная версия метода коллокации позволила достичь точности решения уравнений, близкой к уровню машинных ошибок округления. Программный продукт, реализующий предложенную p-версию, получился достаточно компактным, а метод оказался экономичным: машинное время, необходимое для решения рассмотренных в работе задач, не превышало 3 секунды работы персонального компьютера. Описан алгоритм, позволяющий оценить точность приближенного решения по предложенной p-версии метода в тех случаях, когда точное решение интегрального уравнения неизвестно. Ключевые слова: интегральное уравнение Фредгольма второго рода, метод коллокации, число обусловленности, квадратура Гаусса.
Вычислительные методы и программирование, Jun 26, 2013
Lecture Notes in Computer Science, 2021
Energy and Power Engineering, 2010
The influence of technological process parameters (aiming angle and implantation energy) on the d... more The influence of technological process parameters (aiming angle and implantation energy) on the distributions of dopant concentrations in a silicon substrate is investigated by computer modeling.
Birkhäuser Boston eBooks, 1999
ABSTRACT This chapter deals with incompressible ideal fluid flows. While choosing the material, t... more ABSTRACT This chapter deals with incompressible ideal fluid flows. While choosing the material, the authors aimed at presenting those reults that have now become the classical results and are widely used in the current research work of the aerohydrodynamicists1-9. In particular, the Bernoulli and Lagrange integrals are derived in Section 4.1. They enable one to find the pressure distribution in the fluid from a given velocity field.
Birkhäuser Boston eBooks, 1999
In this chapter, we consider the similarity and dimensional methods, including the construction o... more In this chapter, we consider the similarity and dimensional methods, including the construction of self-similar solutions. We also present the theory of weak discontinuities (the characteristics) and strong discontinuities (shock waves and tangential discontinuities).
International Journal for Numerical Methods in Fluids, May 1, 1984
We consider a problem on shock wave localization in the numerical solution of one‐dimensional uns... more We consider a problem on shock wave localization in the numerical solution of one‐dimensional unsteady problems of gas dynamics in Eulerian variables obtained on the basis of finite difference shock‐capturing schemes. An optimization method for strong discontinuity localization proposed previously by Miranker and Pironneau is investigated by means of methods of classical variational calculus. This method may be difficult to implement when the entropy condition is included in the formulation of Miranker and Pironneau's optimization problem as an active constraint. In this connection we suggest an alternative optimization problem using artificial viscosity in the variational principle. It is shown theoretically that the application of such a variational principle yields a trajectory which coincides with the true discontinuity trajectory in the case of a shock wave moving at a constant speed. On the basis of this modification one more algorithm is proposed which reduces the shock localization problem to a problem of minimization of a univariate function. Numerical tests corroborate completely the theoretical conclusions. In particular, a higher shock localization accuracy is obtained on the basis of the proposed algorithms as compared to the original Miranker‐Pironneau method.
Journal of Mining Science, Mar 1, 1973
ABSTRACT
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Papers by Evgenii Vorozhtsov