Article Frontmatter was published on June 1, 2021 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 36, issue 3).

New solution algorithms of optimal filtering problem are proposed for systems with random structure and continuous time. This problem consists in estimating the current state of system based on the results of measurements. The mathematical model of the system includes nonlinear stochastic differential equations whose right-hand side determines the structure of the dynamic system or mode of operation

High precision simulation algorithms are proposed and justified for modelling cold plasma oscillations taking into account electron–ion collisions in the non-relativistic case. The specific feature of the approach is the use of Lagrangian variables for approximate solution of the problem formulated initially in Eulerian variables. High accuracy is achieved both through the use of analytical solutions

A new mathematical model of the diffusion–convective process with ‘memory along the flow path’ is proposed. This process is described by a homogeneous one-dimensional Dirichlet initial-boundary value problem with a fractional derivative along the characteristic curve of the convection operator. A finite-difference approximation of the problem is constructed and investigated. The stability estimates

This work presents a new approach to modelling of free surface non-Newtonian (viscoplastic or viscoelastic) fluid flows on dynamically adapted octree grids. The numerical model is based on the implicit formulation and the staggered location of governing variables. We verify our model by comparing simulations with experimental and numerical results known from the literature.

In this paper we consider the problem of modelling a system of aggregating particles, that are being transported with stationary velocities dependent on masses of the particles in one-dimensional case. A numerical method based on the ideas of POD (Proper Orthogonal Decomposition) is constructed, and its capacity to speed up the solution up to 40 times is demonstrated.

Article Frontmatter was published on April 1, 2021 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 36, issue 2).

The work is devoted to the application of Runge–Kutta discontinuous Galerkin (RKDG) method for solving Baer–Nunziato hyperbolic model for nonequilibrium two-phase flows. The approach is based on the application of the simple WENO limiter directly to the conservative variables. Mathematical model and the corresponding numerical algorithm are described. The results of numerical simulations for 1D and

The paper is focused on construction of computational models of stratus clouds using remote sensing data and on Monte Carlo analysis of optical radiation transfer peculiarities caused by stochastic structure of clouds.

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 the relaxation method for forming an approximate periodic

Turbulent mixing, ignition, and flame stabilization in the non-premixed supersonic hydrogen-air flow is numerically modelled in a near-wall region. Mixing algorithm based on the turbulence approach SARANS (Reynolds Averaged Navier–Stokes equations closed with Spalart–Allmaras turbulence model) with a diffusion model and a detailed kinetic model for hydrogen-air chemical reactions are employed. The

Ensemble numerical experiments for winter seasons of 1980–2014 were carried out with the use of the mathematical climate model of the Institute of Numerical Mathematics (INM) of the Russian Academy of Sciences developed initially for multi-year climate forecasts. Based on the results obtained in this research, a qualitative assessment of the reproduction of the North Atlantic (NAO) and Pacific-North

Article Frontmatter was published on February 1, 2021 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 36, issue 1).

We suggest an algorithm for construction of semi-structured thick prismatic mesh layers which guarantees an absence of inverted prismatic cells in resulting layer and allows one to control near-surface mesh orthogonality. Initial mesh is modelled as a thin layer of highly compressed prisms made of hyperelastic material glued to the triangulated surface. In order to compute robust normals at the vertices

The paper discusses the numerical algorithm constructing a three-dimensional model for a flow of two-phase incompressible fluid caused by the mass force of gravity in a porous medium. The algorithm is based on a combination of a hybrid upwind method with an explicit scheme for determination of the saturation. The hybrid upwinding allows us to take into account flows of fluid of various nature (in this

The paper presents the results of comparison of various methods of spatial interpolation of the wind chill index in two regions located in the South of Western Siberia (Russia). It is shown that stochastic interpolation provides the least interpolation error in the considered regions. The results of modelling the spatial and spatio-temporal fields of the considered bioclimatic index on a regular grid

For the model of ocean thermodynamics developed at the Institute of Numerical Mathematics of RAS, the problem of variational data assimilation is considered in order to restore heat fluxes on the ocean surface and initial state of the model. Iterative solution algorithms are proposed for the optimality system, justification of these algorithms is given based on properties of the control operator. The

Article Corrigendum to: Mathematical immunology: from phenomenological to multiphysics modelling was published on February 1, 2021 in the journal Russian Journal of Numerical Analysis and Mathematical Modelling (volume 36, issue 1).

Abstract 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.

Abstract 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

Abstract 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

Abstract 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

Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 6 Pages: i-iii

Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 5 Pages: i-iii

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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.

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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.

Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 4 Pages: 187-187

Journal Name: Russian Journal of Numerical Analysis and Mathematical Modelling Volume: 35 Issue: 4 Pages: i-iii

Abstract This paper is a continuation of [38]. 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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.

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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

Abstract 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 the scales and forms of the optimal disturbances

Abstract In the present work the possibility of turbulence closure applying to improve barotropic jet instability simulation at coarse grid resolutions is considered. This problem is analogous to situations occurring in eddy-permitting ocean models when Rossby radius of deformation is partly resolved on a computational grid. We show that the instability is slowed down at coarse resolutions. As follows

Abstract The paper deals with the problem of the equatorial ionization anomaly (EIA) modelling and its representation in the global dynamical models of Earth’s ionosphere and thermosphere. A new version of the coupled thermosphere-ionosphere global dynamical model which reproduce the equatorial anomaly considerably well is presented. Key processes responsible for the EIA formation are outlined and

Abstract Algorithms of Monte Carlo method for estimating probabilistic moments of the parameter of time exponential asymptotics of particle flux with multiplication in a random medium are constructed. It was analytically and numerically shown that the asymptotics of the mean number of particles is close to an exponential one with the factor containing a summand proportional to square of time.

Abstract The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a layer 0 < z < H with given one-dimensional distribution and correlation function of the integral over coordinate z is solved. The gamma distribution with shape parameter ν and scale parameter θ is used in the work. An aggregate of n independent elementary horizontal layers of thickness

Abstract A numerical model for the investigation of hydrodynamic stability of viscous incompressible shear flows in pipes of constant elliptic cross-section is proposed. The model is supplied with efficient algorithms for computing various hydrodynamic stability characteristics including the maximum possible amplification of the average kinetic energy density of disturbances and the so-called optimal

Abstract We consider a method due to P. Vassilevski and Yu. A. Kuznetsov [4, 10] for solving linear systems with matrices of low Kronecker rank such that all factors in Kronecker products are banded. Most important examples of such matrices arise from discretized div K grad operator with diffusion term k1(x)k2(y)k3(z). Several practical issues are addressed: an MPI implementation with distribution

Abstract A new method is developed to calculate characteristics of contaminant transport (including non-classical regimes) in statistically homogeneous sharply contrasting media. A transport integro-differential equation in the space-time representation is formulated on the basis of the model earlier proposed by one of the authors (L. M.). Analytical expressions for transport characteristics in limiting

Abstract We consider approaches to simulation of periodically correlated random processes based on the nonstandard spectral representation of the process with parameters periodically varying in time and also on spectral representations using the vector stationary Gaussian processes.

Abstract Human knee is one of the most complex joints. Different reasons may lead to knee instability. A personalized mathematical model of the knee may improve both diagnostic procedure and knee surgery outcomes. Such models require accurate geometric representation of bones and attachment sites of ligaments and tendons. This paper addresses automatic segmentation of knee bones and detection of origins

Abstract Aortic valve disease accounts for 45% of deaths from heart valve diseases.% \cite{Coffey2015}. An appealing approach to treat aortic valve disease is surgical replacement of the valve leaflets based on chemically treated autologous pericardium. This procedure is attractive due to its low cost and high effectiveness. We aim to develop a computational technology for patient-specific assessment

Abstract A model of lymph flow in the human lymphatic system in the quasi-one-dimensional approach has been created and investigated under different conditions. The model includes an implementation of contractions and valve influence on lymph flow. We consider contractions of lymphatic vessels and their influence on resulting flow in the whole network of lymphatic vessels and lymph nodes. We have investigated

Abstract The method of constructing a stability indicatrix of a nonnegative matrix having the form of a polynomial of its coefficients is presented. The algorithm of construction and conditions of its applicability are specified. The applicability of the algorithm is illustrated on examples of constructing the stability indicatrix for a series of functions widely used in simulation of the dynamics