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Variational data assimilation for a sea dynamics model 海洋动力模式的变分资料同化
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-06-01 DOI: 10.1515/rnam-2022-0011
V. Agoshkov, V. Zalesny, V. Shutyaev, E. Parmuzin, N. Zakharova
{"title":"Variational data assimilation for a sea dynamics model","authors":"V. Agoshkov, V. Zalesny, V. Shutyaev, E. Parmuzin, N. Zakharova","doi":"10.1515/rnam-2022-0011","DOIUrl":"https://doi.org/10.1515/rnam-2022-0011","url":null,"abstract":"Abstract The 4D variational data assimilation technique is presented for modelling the sea dynamics problems, developed at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS). The approach is based on the splitting method for the mathematical model of sea dynamics and the minimization of cost functionals related to the observation data by solving an optimality system that involves the adjoint equations and observation and background error covariances. Efficient algorithms for solving the variational data assimilation problems are presented based on iterative processes with a special choice of iterative parameters. The technique is illustrated for the Black Sea dynamics model with variational data assimilation to restore the sea surface heat fluxes.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49108249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mesh scheme for a phase transition problem with time-fractional derivative 一类具有时间分数导数的相变问题的网格格式
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-06-01 DOI: 10.1515/rnam-2022-0013
A. Lapin
{"title":"Mesh scheme for a phase transition problem with time-fractional derivative","authors":"A. Lapin","doi":"10.1515/rnam-2022-0013","DOIUrl":"https://doi.org/10.1515/rnam-2022-0013","url":null,"abstract":"Abstract The time-fractional phase transition problem, formulated in enthalpy form, is studied. This nonlinear problem with an unknown moving boundary includes, as an example, a mathematical model of one-phase Stefan problem with the latent heat accumulation memory. The posed problem is approximated by the backward Euler mesh scheme. The unique solvability of the mesh scheme is proved and a priori estimates for the solution are obtained. The properties of the mesh problem are studied, in particular, an estimate of movement rate for the mesh phase transition boundary is established. The proved estimate make it possible to localize the phase transition boundary and split the mesh scheme into the sum of a nonlinear problem of small algebraic dimension and a larger linear problem. This information can be used for further construction of efficient algorithms for implementing the mesh scheme. Several algorithms for implementing mesh scheme are briefly discussed.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44817096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the multi-annual potential predictability of the Arctic Ocean climate state in the INM RAS climate model 关于INM-RAS气候模型中北冰洋气候状态的多年潜在可预测性
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0010
E. Volodin, V. Vorobyeva
{"title":"On the multi-annual potential predictability of the Arctic Ocean climate state in the INM RAS climate model","authors":"E. Volodin, V. Vorobyeva","doi":"10.1515/rnam-2022-0010","DOIUrl":"https://doi.org/10.1515/rnam-2022-0010","url":null,"abstract":"Abstract Idealized numerical experiments with the INM RAS climate model are used to study the potential predictability of the temperature in the upper 300-meter layer of the Arctic Ocean. It is shown that the heat content can be predictable for up to 4–6 years. Positive anomalies of the temperature and salinity are preceded for several years by a state in which the influx of Atlantic water into the Arctic Ocean exceeds the average value. Surface fields, including temperature, salinity, concentration and mass of ice, are less predictable than the heat content in the layer of 0–300 meters.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46289726","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Development of a numerical stochastic model of joint spatio-temporal fields of weather parameters for the south part of the Baikal natural territory 贝加尔湖自然区南部天气参数时空联合场数值随机模型的建立
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0006
M. S. Akenteva, N. Kargapolova, V. Ogorodnikov
{"title":"Development of a numerical stochastic model of joint spatio-temporal fields of weather parameters for the south part of the Baikal natural territory","authors":"M. S. Akenteva, N. Kargapolova, V. Ogorodnikov","doi":"10.1515/rnam-2022-0006","DOIUrl":"https://doi.org/10.1515/rnam-2022-0006","url":null,"abstract":"Abstract The paper is focused on the construction of a numerical stochastic model of the joint spatio-temporal fields of air temperature, wind speed vector with three-hour resolution, and semidiurnal precipitation amounts according to observation data at a group of weather stations located in the south of the Baikal natural territory. The model also takes into account the dependence of one-dimensional distributions on temporal and spatial coordinates. The heterogeneity of the field in spatial correlations and the periodical correlation in time are also taken into account. The results of calculations for verification of the model are presented. An example of using the developed model to study the properties of time series of the wind chill index is given.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46037937","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Frontmatter Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-frontmatter2
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2022-frontmatter2","DOIUrl":"https://doi.org/10.1515/rnam-2022-frontmatter2","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48557880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Discrete curvatures for planar curves based on Archimedes’ duality principle 基于阿基米德对偶原理的平面曲线的离散曲率
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0007
V. Garanzha, L. Kudryavtseva, Dmitry A. Makarov
{"title":"Discrete curvatures for planar curves based on Archimedes’ duality principle","authors":"V. Garanzha, L. Kudryavtseva, Dmitry A. Makarov","doi":"10.1515/rnam-2022-0007","DOIUrl":"https://doi.org/10.1515/rnam-2022-0007","url":null,"abstract":"Abstract We introduce discrete curvatures for planar curves based on the construction of sequences of pairs of mutually dual polylines. For piecewise-regular curves consisting of a finite number of fragments of regular generalized spirals with definite (positive or negative) curvatures our discrete curvatures approximate the exact averaged curvature from below and from above. In order to derive these estimates one should provide a distance function allowing to compute the closest point on the curve for an arbitrary point on the plane.With refinement of the polylines, the averaged curvature over refined curve segments converges to the pointwise values of the curvature and, thus, we obtain a good and stable local approximation of the curvature. For the important engineering case when the curve is approximated only by the inscribed (primal) polyline and the exact distance function is not available, we provide a comparative analysis for several techniques allowing to build dual polylines and discrete curvatures and evaluate their ability to create lower and upper estimates for the averaged curvature.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47959941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach 北冰洋热含量变率低频模态的可预测性:一种完美的模式方法
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0008
A. Gritsun
{"title":"Predictability of the low-frequency modes of the Arctic Ocean heat content variability: a perfect model approach","authors":"A. Gritsun","doi":"10.1515/rnam-2022-0008","DOIUrl":"https://doi.org/10.1515/rnam-2022-0008","url":null,"abstract":"Abstract The problem of potential predictability of the temperature of the upper layer of the Arctic Ocean for the data of pre-industrial climate modelling run by the INM-CM5 Earth system model developed at the INM RAS is considered. The main attention is paid to the analysis of predictability of the phases of the dominant modes of low-frequency variability of the Arctic Ocean circulation. The initial estimate of its predictability is made by using the method of analogues and calculating the resonances of the invariant measure. Then this estimate is verified by direct ensemble calculations with the model. The results obtained indicate that the maximum predictability time interval reaches ten years for 15-year average values of heat content and corresponds to the states with maximum positive anomalies along the leading low-frequency variability modes.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46346036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal stochastic forcings for sensitivity analysis of linear dynamical systems 线性动力系统灵敏度分析的最优随机强迫
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-04-01 DOI: 10.1515/rnam-2022-0009
Y. Nechepurenko, G. Zasko
{"title":"Optimal stochastic forcings for sensitivity analysis of linear dynamical systems","authors":"Y. Nechepurenko, G. Zasko","doi":"10.1515/rnam-2022-0009","DOIUrl":"https://doi.org/10.1515/rnam-2022-0009","url":null,"abstract":"Abstract The paper is devoted to the construction of optimal stochastic forcings for studying the sensitivity of linear dynamical systems to external perturbations. The optimal forcings are sought to maximize the Schatten norms of the response. As an example,we consider the problem of constructing the optimal stochastic forcing for the linear dynamical system arising from the analysis of large-scale structures in a stratified turbulent Couette flow.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44229731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method 传递矩阵与气溶胶团簇随机动力学问题的蒙特卡罗解法
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0001
A. Cheremisin
{"title":"Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method","authors":"A. Cheremisin","doi":"10.1515/rnam-2022-0001","DOIUrl":"https://doi.org/10.1515/rnam-2022-0001","url":null,"abstract":"Abstract A Monte Carlo algorithm based on the use of transfer matrices is developed to describe the stochastic dynamics of the rotational--translational motion of aerosol clusters taking into account fluctuations in the molecular fluxes of the gas medium. In the general case, the cluster is immersed into a rarefied gas medium, the temperatures of its surfaces may differ from the temperature of the surrounding gas, for example, due to absorption of visible and infrared radiation. The motion of the cluster is described based on Langevin motion equations. The algorithm allows one to calculate parameters of the probability distribution of a six-dimensional vector consisting of components of the momentum and angular momentum vectors transmitted to the cluster by molecular flows. The numerical method allows one to apply preliminary analytical averaging modulo velocities of molecules for both the average values of the components of momentum and angular momentum and their correlation characteristics, which significantly reduces the calculation time.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44597766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field 保留地磁场方向的电离层模型中扩散算子的近似
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-02-01 DOI: 10.1515/rnam-2022-0003
P. A. Ostanin
{"title":"On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field","authors":"P. A. Ostanin","doi":"10.1515/rnam-2022-0003","DOIUrl":"https://doi.org/10.1515/rnam-2022-0003","url":null,"abstract":"Abstract New methods for constructing an approximation of the diffusion operator for the two-dimensional equation of the ambipolar diffusion process in the F layer of the Earth's ionosphere are presented. This equation is solved in the framework of modelling the global thermosphere and ionosphere dynamics (for the altitudes from 90 to 500 km). The proposed schemes have finite-difference versions of the integral identity, which is a property of differential diffusion equation and which represents the geometric properties of the process (diffusion proceeds along the magnetic field lines of the Earth). The stability of the proposed schemes is analyzed, as well as the accuracy estimates are obtained on the base of the model analytical solution and during the calculations with physically realistic data. A comparison is made with the second-order finite-difference scheme developed earlier for solving the same problem.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48801876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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