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).

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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)

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

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

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

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

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

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

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.

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

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

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

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

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