Published since January 1, 1986

Russian Journal of Numerical Analysis and Mathematical Modelling

ISSN: 1569-3988

Editors-in-chief: Valentin P. Dymnikov, Yuri A. Kuznetsov

Managing Editor: Yuri V. Vassilevski

Impact Factor: 1.161

About this journal

Objective
The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest.

Topics

numerical analysis
numerical linear algebra
finite element methods for PDEs
iterative methods
Monte-Carlo methods
mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences

Article formats
Research articles

> Information on submission process

Your Benefits

Your benefits:

State-of-the-art original Russian papers in the field of numerical analysis and mathematical modelling translated in English
Imperative topics of high interest and relevance to the international research community
Leading Russian experts as members of the Editorial Board

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Publication Ethics and Malpractice Statement

Volume 36 Issue 4

August 2021

Accessible October 4, 2021

Frontmatter

Page range: i-iii

Download PDF

October 4, 2021

Comparison of nonlinear solvers within continuation method for steady-state variably saturated groundwater flow modelling

Denis Anuprienko

Page range: 183-195

Abstract

Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search algorithm was used to solve the intermediate problems. In the present paper, other solvers such as Picard and mixed Picard–Newton methods are considered, combined with slightly modified line search approach. Numerical experiments are performed with advanced finite volume discretizations for model and real-life problems.

October 4, 2021

A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations

Vladislav Balashov

Page range: 197-217

Abstract

The present paper is devoted to a model describing a two-phase isothermal mixture, in which one of the phases obeys solid-like (namely, elastic) rheology. A fully Eulerian description is considered. To describe the stress–strain behaviour of the solid phase the elastic energy term is added to the Helmholtz free energy. The term depends on Almansi strain tensor. In its turn, the strain tensor is defined as the solution of the corresponding evolutionary equation. Considered model belongs to the phase field family. Formally it describes two-component mixture and uses mass densities of the components as order parameters. A distinctive feature of the considered model is its preliminary regularization according to the quasi-hydrodynamic framework. The dissipativity in total energy is proved when periodic boundary conditions are imposed. A spatial dissipative semi-discrete (continuous in time and discrete in space) scheme based on staggered grids is suggested. The theoretical results remain valid in the absence of the regularization. The results of a numerical study in a 2D setting are presented.

October 4, 2021

New correlative randomized algorithms for statistical modelling of radiation transfer in stochastic medium

Guennady A. Mikhailov, Ilia N. Medvedev

Page range: 219-225

Abstract

Correlative randomized algorithms are constructed by simple randomization of the algorithm of maximum cross-section (equalization, delta tracking) with the use of a one-dimensional distribution and the correlation function or only correlation length of a random medium. The value of the used correlation length can be adjusted using simple test studies. The calculations carried out confirmed the practical effectiveness of the new algorithms.

October 4, 2021

The suite of Taylor–Galerkin class schemes for ice transport on sphere implemented by the INMOST package

Sergey S. Petrov, Nikolay G. Iakovlev

Page range: 227-238

Abstract

Realizations of the numerical solution of the scalar transport equation on the sphere, written in divergent form, are presented. Various temporal discretizations are considered: the one-step Taylor–Galerkin method (TG2), the two-step Taylor–Galerkin method of the second (TTG2), third (TTG3), and fourth (TTG4) orders. The standard Finite-Element Galerkin method with linear basis functions on a triangle is applied as spatial discretization. The flux correction technique (FCT) is implemented. Test runs are carried out with different initial profiles: a function from C ∞ (Gaussian profile) and a discontinuous function (slotted cylinder). The profiles are advected by reversible, nondivergent velocity fields, therefore the initial distribution coincides with the final one. The case of a divergent velocity field is also considered to test the conservation and positivity properties of the schemes. It is demonstrated that TG2, TTG3, and TTG4 schemes with FCT applied give the best result for small Courant numbers, and TTG2, TTG4 are preferable in case of large Courant number. However, TTG2+FCT scheme has the worst stability. The use of FCT increases the integral errors, but ensures that the solution is positive with high accuracy. The implemented schemes are included in the dynamic core of a new sea ice model developed using the INMOST package. The acceleration of the parallel program and solution convergence with spatial resolution are demonstrated.

October 4, 2021

Stability analysis of implicit semi-Lagrangian methods for numerical solution of non-hydrostatic atmospheric dynamics equations

Vladimir V. Shashkin

Page range: 239-253

Abstract

The stability of implicit semi-Lagrangian schemes for time-integration of the non-hydrostatic atmosphere dynamics equations is analyzed in the present paper. The main reason for the instability of the considered class of schemes is the semi-Lagrangian advection of stratified thermodynamic variables coupled to the fixed point iteration method used to solve the implicit in time upstream trajectory computation problem. We identify two types of unstable modes and obtain stability conditions in terms of the scheme parameters. Stabilization of sound modes requires the use of a pressure reference profile and time off-centering. Gravity waves are stable only for an even number of fixed point method iterations. The maximum time step is determined by inverse buoyancy frequency in the case when the reference profile of the potential temperature is not used. Generally, applying time off-centering and reference profile to pressure variable is necessary for stability. Using reference profile for potential temperature and an even number of the iterations allows one to significantly increase the maximum time-step value.

Volume 36 (2021)

Volume 35 (2020)

Volume 34 (2019)

Volume 33 (2018)

Volume 32 (2017)

Volume 31 (2016)

Volume 30 (2015)

Volume 29 (2014)

Volume 28 (2013)

Volume 27 (2012)

Volume 26 (2012)

Volume 25 (2010)

Volume 24 (2009)

Volume 23 (2008)

Volume 22 (2007)

Volume 21 (2006)

Volume 20 (2005)

Volume 19 (2004)

Volume 18 (2003)

Volume 17 (2002)

Volume 16 (2001)

Volume 15 (2000)

Volume 14 (1999)

Volume 13 (1998)

Volume 12 (1997)

Volume 11 (1996)

Volume 10 (1995)

Volume 9 (1994)

Volume 8 (1993)

Volume 7 (1992)

Volume 6 (1991)

Volume 5 (1990)

Volume 4 (1989)

Volume 3 (1988)

Volume 2 (1987)

Volume 1 (1986)

5-year Impact Factor	0.914
Cite Score	1.9
Impact Factor	1.161
Journal Citation Indicator	0.54
Mathematical Citation Quotient	0.20
SCImago Journal Rank	0.523
Source Normalized Impact per Paper	1.373

Submit

Submission
The contents of the Russian Journal of Numerical Analysis and Mathematical Modeling is based on the results of research conducted in the Russian Federation. To this end, the Editorial Board considers for publication primarily papers in which at least one of the authors is a citizen of Russia. The Editorial Board also considers papers based on research conducted by Russian scientists outside of Russia. The papers can be submitted via e-mail to the Managing Editor written either in Russian or English language.

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Submission process

Submission of your manuscript
Peer review process (you will be guided through every step)
Decision on your paper
If accepted: you have the option to publish it open access
Publication online and in print

Please note

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Once your article is accepted you have the option to publish it open access
Our repository policy allows you to distribute 30 PDF copies of your published article to colleagues (the PDF has to include the information that it is an author's copy). Please also feel free to distribute the link to the online abstract
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Hybrid Open Access

Please note that authors from institutions with which we have a transformative agreement can publish open access without paying an article processing charge (APC). More information on the eligible institutions and articles can be found under the "Funding and Support" tab here

Editorial

EDITORS-IN-CHIEF
Valentin P. Dymnikov,  Moscow
Yuri A. Kuznetsov,  Houston/Moscow

MANAGING EDITOR 
Yuri V. Vassilevski, Moscow
Institute of Numerical Mathematics of Russian Academy of Sciences Gubkina str. 8
Moscow 119333, Russia
Email: journal [at] dodo.inm.ras.ru

EDITORIAL BOARD 
Valery I. Agoshkov,  Moscow
Vladimir A. Garanzha, Moscow
Nikolay G. Iakovlev, Moscow
Georgy M. Kobelkov, Moscow
Gennady A. Mikhailov,  Moscow
Yuri M. Nechepurenko, Moscow
Sergey I. Repin, St. Petersburg
Vladimir V. Shaidurov,  Krasnojarsk
Yurii I. Shokin,  Novosibirsk
Eugene E. Tyrtyshnikov, Moscow

(Deutsch)

Online ISSN: 1569-3988
Print ISSN: 0927-6467
Type: Journal
Language: English
Publisher: De Gruyter
First published: January 1, 1986
Publication Frequency: 6 Issues per Year
Audience: researchers in the field of numerical analysis and mathematical modelling