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Numerical simulation of optical phenomena in atmospheric clouds and fogs Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-12-09 Andrey V. Zakovryashin; Sergei M. Prigarin
We present algorithms for fast computation of phase functions of atmospheric clouds and for stochastic simulation of such optical phenomena as fogbows, glories, coronas and halos. Using the developed numerical algorithms and software, we analyze optical phenomena for several cloud and fog models.
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Semi-Lagrangian exponential time-integration method for the shallow water equations on the cubed sphere grid Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-12-09 Vladimir V. Shashkin; Gordey S. Goyman
This paper proposes the combination of matrix exponential method with the semi-Lagrangian approach for the time integration of shallow water equations on the sphere. The second order accuracy of the developed scheme is shown. Exponential semi-Lagrangian scheme in the combination with spatial approximation on the cubed-sphere grid is verified using the standard test problems for shallow water models
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A new kernel-projective statistical estimator in the Monte Carlo method Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-12-09 Gennady A. Mikhailov; Natalya V. Tracheva; Sergey A. Ukhinov
In the present paper, we propose a new combined kernel-projective statistical estimator of the two-dimensional distribution density, where the first ‘main’ variable is processed with the kernel estimator, and the second one is processed with the projective estimator for the conditional distribution density. In this case, statistically estimated coefficients of some orthogonal expansion of the conditional
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Simulation of proppant transport and fracture plugging in the framework of a radial hydraulic fracturing model Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-12-09 Vasily N. Lapin; Denis V. Esipov
Hydraulic fracturing technology is widely used in the oil and gas industry. A part of the technology consists in injecting a mixture of proppant and fluid into the fracture. Proppant significantly increases the viscosity of the injected mixture and can cause plugging of the fracture. In this paper we propose a numerical model of hydraulic fracture propagation within the framework of the radial geometry
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Frontmatter Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-12-09
Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 6 Pages: i-iii
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A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30 Yuri Vassilevski; Alexander Danilov; Alexander Lozovskiy; Maxim Olshanskii; Victoria Salamatova; Su Min Chang; Yushui Han; Chun Huie Lin
The paper discusses a stabilization of a finite element method for the equations of fluid motion in a time-dependent domain. After experimental convergence analysis, the method is applied to simulate a blood flow in the right ventricle of a post-surgery patient with the transposition of the great arteries disorder. The flow domain is reconstructed from a sequence of 4D CT images. The corresponding
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Analysis of the impact of left ventricular assist devices on the systemic circulation Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30 Sergey S. Simakov; Alexander E. Timofeev; Timur M. Gamilov; Philipp Yu. Kopylov; Dmitry V. Telyshev; Yuri V. Vassilevski
In this work we analyze the impact of left ventricular assist devices on the systemic circulation in subjects with heart failure associated with left ventricular dilated cardiomyopathy. We use an integrated model of the left heart and blood flow in the systemic arteries with a left ventricular assist device. We study the impact of the rotation speed of the pump on haemodynamic characteristics of distal
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Spatially averaged haemodynamic models for different parts of cardiovascular system Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30 Sergey S. Simakov
This paper revisits the usage of spatially averaged haemodynamic models such as non-stationary 1D/0D in space and stationary 0D in space models. Conditions of equivalence between different 1D model formulations are considered. The impact of circular and elliptic shapes of the tube cross-section on the friction term and the tube law is analyzed. Finally, the relationship between 0D lumped and 1D models
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Induced drift of scroll waves in the Aliev–Panfilov model and in an axisymmetric heart left ventricle Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30 Sergei F. Pravdin; Timofei I. Epanchintsev; Timur V. Nezlobinskii; Alexander V. Panfilov
The low-voltage cardioversion-defibrillation is a modern sparing electrotherapy method for such dangerous heart arrhythmias as paroxysmal tachycardia and fibrillation. In an excitable medium, such arrhythmias relate to appearance of spiral waves of electrical excitation, and the spiral waves are superseded to the electric boundary of the medium in the process of treatment due to high-frequency stimulation
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Application of mutual information estimation for predicting the structural stability of pentapeptides Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30 A. I. Mikhalskii; I. V. Petrov; V. V. Tsurko; A. A. Anashkina; A. N. Nekrasov
A novel non-parametric method for mutual information estimation is presented. The method is suited for informative feature selection in classification and regression problems. Performance of the method is demonstrated on problem of stable short peptide classification.
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Frontmatter Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-10-30
Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 5 Pages: i-iii
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Global optimization based on TT-decomposition Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Dmitry Zheltkov; Eugene Tyrtyshnikov
In contrast to many other heuristic and stochastic methods, the global optimization based on TT-decomposition uses the structure of the optimized functional and hence allows one to obtain the global optimum in some problem faster and more reliable. The method is based on the TT-cross method of interpolation of tensors. In this case, the global optimum can be found in practice even in the case when
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Tensor decompositions and rank increment conjecture Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Eugene E. Tyrtyshnikov
Some properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding
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Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Kirill M. Terekhov
This work presents an overview of techniques that enable the construction of collocated finite volume method for complex multi-physics models in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. Coupling together systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume
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Iterative solution methods for elliptic boundary value problems Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Georgy M. Kobelkov
For elliptic boundary value problems (the diffusion equation and elasticity theory ones) with highly varying coefficients, there are proposed iterative methods with the number of iterations independent of the coefficient jumps. In the differential case these methods take solving the boundary value problem for the Poisson equation at each step of iterations while in the finite difference (finite element)
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Mathematical immunology: from phenomenological to multiphysics modelling Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Gennady A. Bocharov; Dmitry S. Grebennikov; Rostislav S. Savinkov
Mathematical immunology is the branch of mathematics dealing with the application of mathematical methods and computational algorithms to explore the structure, dynamics, organization and regulation of the immune system in health and disease. We review the conceptual and mathematical foundation of modelling in immunology formulated by Guri I. Marchuk. The current frontier studies concerning the development
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Methods of variational data assimilation with application to problems of hydrothermodynamics of marine water areas Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13 Valery I. Agoshkov; Natalia R. Lezina; Eugene I. Parmuzin; Tatiana O. Sheloput; Victor P. Shutyaev; Natalia B. Zakharova
A series of problems related to the class of inverse problems of ocean hydrothermodynamics and problems of variational data assimilation are formulated in the present paper. We propose methods for solving the problems studied here and present results of numerical experiments.
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Preface Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13
Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 4 Pages: 187-187
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Frontmatter Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-08-13
Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 4 Pages: i-iii
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High order modified differential equation of the Beam–Warming method, II. The dissipative features Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-06-04 Yurii Shokin; Ireneusz Winnicki; Janusz Jasinski; Slawomir Pietrek
This paper is a continuation of []. The analysis of the modified partial differential equation (MDE) of the constant-wind-speed linear advection equation explicit difference scheme up to the eighth-order derivatives is presented. In this paper the authors focus on the dissipative features of the Beam–Warming scheme. The modified partial differential equation is presented in the so-called Π-form of
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Hyperelastic membrane modelling based on data-driven constitutive relations Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-06-04 Victoria Yu. Salamatova; Alexey A. Liogky
We present data-driven modelling of membrane deformation by a hyperelastic nodal force method. We assume that constitutive relations are characterized by tabulated experimental data instead of the conventional phenomenological approach. As experimental data we use synthetic data from the bulge test simulation for neo-Hookean and Gent materials. The numerical study of descriptive and predictive capabilities
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Randomized exponential transformation algorithm for solving the stochastic problems of gamma-ray transport theory Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-06-04 Ilia N. Medvedev; Gennadii A. Mikhailov
The paper presents a new algorithm of exponential transformation and its randomized modification with branching of a Markov chain trajectory for solving the problem of gamma-ray transport. Based on the example of radiation transfer in water, numerical study of presented algorithms is performed in comparison with standard simulation algorithms. The study of the influence of medium stochasticity on the
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Double randomization method for estimating the moments of solution to vehicular traffic problems with random parameters Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-06-04 Aleksandr Burmistrov; Mariya Korotchenko
In this paper we consider a Boltzmann type equation arising in the kinetic vehicle traffic flow model with an acceleration variable. The latter model is improved within the framework of the previously developed approach by introducing a set of random parameters. This enables us to take into account different types of interacting vehicles, as well as various parameters describing skills and behavior
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Discrete and asymptotic approximations for one stationary radiative–conductive heat transfer problem Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-06-04 Andrey A. Amosov; Nikita E. Krymov
Special discrete and asymptotic approximations are proposed for the boundary value problem describing a stationary radiative–conductive heat transfer in a system of absolutely black heat-conducting rods of circular cross-section. Results of numerical experiments are presented to confirm the efficiency of proposed approximations.
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Mathematical modelling of acute phase of myocardial infarction Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-04-28 Chermen A. Tsgoev; Olga F. Voropaeva; Yuri I. Shokin
A mathematical model of the dynamics of cardiomyocyte death in myocardial infarction during the acute phase of the disease is developed. An economical computing technology of structural and parametric identification of model equations is presented based on the use of experimental data as dynamic parameters and on the idea of splitting the inverse coefficient problem with a large number of unknown parameters
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Numerical steady state analysis of the Marchuk–Petrov model of antiviral immune response Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-04-28 Ekaterina V. Sklyarova; Yuri M. Nechepurenko; Gennady A. Bocharov
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 nonnegative solutions is analytically localized. An effective
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High order modified differential equation of the Beam–Warming method, I. The dispersive features Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-04-28 Yurii Shokin; Ireneusz Winnicki; Janusz Jasinski; Slawomir Pietrek
The analysis of the modified partial differential equation (MDE) of the constant wind speed advection equation explicit difference scheme up to the eighth order with respect to both space and time derivatives is presented. So far, in majority of publications this modified equation has been derived mainly as a fourth-order equation. The MDE is presented in the so-called Π-form of the first differential
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Testing of kinetic energy backscatter parameterizations in the NEMO ocean model Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-04-28 Pavel A. Perezhogin
Eddy-permitting numerical ocean models resolve mesoscale turbulence only partly, that leads to underestimation of eddy kinetic energy (EKE). Mesoscale dynamics can be amplified by using kinetic energy backscatter (KEB) parameterizations returning energy from the unresolved scales. We consider two types of KEB: stochastic and negative viscosity ones. The tuning of their amplitudes is based on a local
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Using maximum cross section method for filtering jump-diffusion random processes Russ. J. Numer. Anal. Math. Model. (IF 0.439) Pub Date : 2020-04-28 Tatyana A. Averina; Konstantin A. Rybakov
The paper is focused on problem of filtering random processes in dynamical systems whose mathematical models are described by stochastic differential equations with a Poisson component. The solution of a filtering problem supposes simulation of trajectories of solutions to a stochastic differential equation. The trajectory modelling procedure includes simulation of a Poisson flow permitting application