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General finite-volume framework for saddle-point problems of various physics 各种物理鞍点问题的一般有限体积框架
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0029
K. Terekhov
{"title":"General finite-volume framework for saddle-point problems of various physics","authors":"K. Terekhov","doi":"10.1515/rnam-2021-0029","DOIUrl":"https://doi.org/10.1515/rnam-2021-0029","url":null,"abstract":"Abstract This article is dedicated to the general finite-volume framework used to discretize and solve saddle-point problems of various physics. The framework applies the Ostrogradsky–Gauss theorem to transform a divergent part of the partial differential equation into a surface integral, approximated by the summation of vector fluxes over interfaces. The interface vector fluxes are reconstructed using the harmonic averaging point concept resulting in the unique vector flux even in a heterogeneous anisotropic medium. The vector flux is modified with the consideration of eigenvalues in matrix coefficients at vector unknowns to address both the hyperbolic and saddle-point problems, causing nonphysical oscillations and an inf-sup stability issue. We apply the framework to several problems of various physics, namely incompressible elasticity problem, incompressible Navier–Stokes, Brinkman–Hazen–Dupuit–Darcy, Biot, and Maxwell equations and explain several nuances of the application. Finally, we test the framework on simple analytical solutions.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"359 - 379"},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47028589","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
An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem p-拉普拉斯问题的内罚不连续伽辽金近似的平衡后验误差估计
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0026
R. Hoppe, Youri Iliash
{"title":"An equilibrated a posteriori error estimator for an Interior Penalty Discontinuous Galerkin approximation of the p-Laplace problem","authors":"R. Hoppe, Youri Iliash","doi":"10.1515/rnam-2021-0026","DOIUrl":"https://doi.org/10.1515/rnam-2021-0026","url":null,"abstract":"Abstract We are concerned with an Interior Penalty Discontinuous Galerkin (IPDG) approximation of the p-Laplace equation and an equilibrated a posteriori error estimator. The IPDG method can be derived from a discretization of the associated minimization problem involving appropriately defined reconstruction operators. The equilibrated a posteriori error estimator provides an upper bound for the discretization error in the broken W1,p norm and relies on the construction of an equilibrated flux in terms of a numerical flux function associated with the mixed formulation of the IPDG approximation. The relationship with a residual-type a posteriori error estimator is established as well. Numerical results illustrate the performance of both estimators.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"313 - 336"},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41567420","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
Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model 关于海洋热力学模型输入数据不确定性的变分数据同化中泛函的稳定性分析
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-12-01 DOI: 10.1515/rnam-2021-0028
V. Shutyaev, E. Parmuzin, I. Gejadze
{"title":"Stability analysis of functionals in variational data assimilation with respect to uncertainties of input data for a sea thermodynamics model","authors":"V. Shutyaev, E. Parmuzin, I. Gejadze","doi":"10.1515/rnam-2021-0028","DOIUrl":"https://doi.org/10.1515/rnam-2021-0028","url":null,"abstract":"Abstract The problem of stability and sensitivity of functionals of the optimal solution of the variational data assimilation of sea surface temperature for the model of sea thermodynamics is considered. The variational data assimilation problem is formulated as an optimal control problem to find the initial state and the boundary heat flux. The sensitivity of the response functions as functionals of the optimal solution with respect to the observation data is studied. Computing the gradient of the response function reduces to the solution of a non-standard problem being a coupled system of direct and adjoint equations with mutually dependent initial and boundary values. The algorithm to compute the gradient of the response function is presented, based on the Hessian of the original cost functional. Stability analysis of the response function with respect to uncertainties of input data is given. Numerical examples are presented for the Black and Azov seas thermodynamics model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"347 - 357"},"PeriodicalIF":0.6,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41918039","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
Frontmatter Frontmatter
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-frontmatter5
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2021-frontmatter5","DOIUrl":"https://doi.org/10.1515/rnam-2021-frontmatter5","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46386755","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
Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection 在HIV-1感染的随机模型中感染细胞和病毒粒子在两个淋巴结间转移的数值模拟
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-0024
N. Pertsev, V. Topchii, K. Loginov
{"title":"Numerical modelling of the transition of infected cells and virions between two lymph nodes in a stochastic model of HIV-1 infection","authors":"N. Pertsev, V. Topchii, K. Loginov","doi":"10.1515/rnam-2021-0024","DOIUrl":"https://doi.org/10.1515/rnam-2021-0024","url":null,"abstract":"Abstract The paper is focused on stochastic modelling of the process of transition of infected cells and virions of HIV-1 infection between two lymph nodes. The model is based on the following assumptions: (1) the duration of transition of infected cells and virions between two lymph nodes is set using a time-dependent function, (2) infected cells produce virions in the process of transition between two lymph nodes, (3) infected cells and virions may die when moving between two lymph nodes. The methods of the theory of branching random processes are used to study analytically the model variables. An algorithm for statistical modelling of the number of infected cells and virions in the second lymph node is presented. The results of computational experiments studying the distribution law of the number of virions produced by one infected cell depending on the duration of movement between two lymph nodes are presented.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"293 - 302"},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45439560","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
Numerical evaluation of the effectiveness of coronary revascularization 冠状动脉血运重建有效性的数值评估
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-0025
S. Simakov, T. Gamilov, F. Liang, D. Gognieva, Mariam K. Gappoeva, P. Kopylov
{"title":"Numerical evaluation of the effectiveness of coronary revascularization","authors":"S. Simakov, T. Gamilov, F. Liang, D. Gognieva, Mariam K. Gappoeva, P. Kopylov","doi":"10.1515/rnam-2021-0025","DOIUrl":"https://doi.org/10.1515/rnam-2021-0025","url":null,"abstract":"Abstract In the present paper we construct the model of coronary flow which utilizes the patient’s CT data on both large CA and perfusion. We reconstruct large coronary vessels based on the CT data and extrude possibly invisible vessels from the branches of the left coronary artery so that every terminal point supply every of standardized zone of myocardium. We apply a previously developed and validated 1D model of haemodynamics. Utilizing the patient-specific CTP data for modifying outflow terminal resistance at rest and under stress conditions is the major novelty of the present work. From our results it follows that acceptable values of fractional flow reserve (FFR) after the stenotic treatment may produce false negative output. Therefore healthy FFR values may be observed after ineffective revascularization. We also conclude that microvascular perfusion impairment plays significant role in correct computational estimation of haemodynamic indices before stenotic treatment. The advantage of the presented approach is the availability of transmural perfusion ratio assessment in everyday practice.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"303 - 312"},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47683635","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: 6
Herd immunity levels and multi-strain influenza epidemics in Russia: a modelling study 俄罗斯群体免疫水平和多株流感流行:一项模型研究
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-0023
V. Leonenko
{"title":"Herd immunity levels and multi-strain influenza epidemics in Russia: a modelling study","authors":"V. Leonenko","doi":"10.1515/rnam-2021-0023","DOIUrl":"https://doi.org/10.1515/rnam-2021-0023","url":null,"abstract":"Abstract In the present paper, we consider a compartmental epidemic model which simulates the co-circulation of three influenza strains, A(H1N1)pdm09, A(H3N2), and B, in a population with the history of exposure to these virus strains. A strain-specific incidence data for the model input was generated using long-term weekly ARI incidence and virologic testing data. The algorithm for model calibration was developed as a combination of simulated annealing and BFGS optimization methods. Two simulations were carried out, assuming the absence and the presence of protected individuals in the population, with 2017– 2018 and 2018–2019 epidemic seasons in Moscow as a case study. It was shown that strain-specific immune levels defined by virologic studies might be used in the model to obtain plausible incidence curves. However, different output parameter values, such as fractions of individuals exposed to particular virus strain in the previous epidemic season, can correspond to similar incidence trajectories, which complicates the assessment of herd immunity levels based on the model calibration. The results of the study will be used in the research of the interplay between the immunity formation dynamics and the circulation of influenza strains in Russian cities.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"279 - 291"},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41840094","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
Two-scale haemodynamic modelling for patients with Fontan circulation Fontan循环患者的双尺度血流动力学模型
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-0022
T. Dobroserdova, Y. Vassilevski, S. Simakov, T. Gamilov, A. Svobodov, L. Yurpolskaya
{"title":"Two-scale haemodynamic modelling for patients with Fontan circulation","authors":"T. Dobroserdova, Y. Vassilevski, S. Simakov, T. Gamilov, A. Svobodov, L. Yurpolskaya","doi":"10.1515/rnam-2021-0022","DOIUrl":"https://doi.org/10.1515/rnam-2021-0022","url":null,"abstract":"Abstract Palliation of congenital single ventricle heart defects suggests multi-stage surgical interventions that divert blood flow from the inferior and superior vena cava directly to the right and left pulmonary arteries, skipping the right ventricle. Such system with cavopulmonary anastomoses and single left ventricle is called Fontan circulation, and the region of reconnection is called the total cavopulmonary connection (TCPC). Computational blood flow models allow clinicians to predict the results of the Fontan operation, to choose an optimal configuration of TCPC and thus to reduce negative postoperative consequences. We propose a two-scale (1D3D) haemodynamic model of systemic circulation for a patient who has underwent Fontan surgical operation. We use CT and 4D flow MRI data to personalize the model. The model is tuned to patient’s data and is able to represent measured time-averaged flow rates at the inlets and outlets of TCPC, as well as pressure in TCPC for the patient in horizontal position.We demonstrate that changing to quiescent standing position leads to other patterns of blood flow in regional (TCPC) and global haemodynamics. This confirms clinical data on exercise intolerance of Fontan patients.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"267 - 278"},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49603452","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
Frontiers in mathematical modelling of the lipid metabolism under normal conditions and its alterations in heart diseases 正常情况下脂质代谢的数学模型及其在心脏病中的变化的前沿
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-11-01 DOI: 10.1515/rnam-2021-0021
G. Bocharov, D. Grebennikov, R. Savinkov
{"title":"Frontiers in mathematical modelling of the lipid metabolism under normal conditions and its alterations in heart diseases","authors":"G. Bocharov, D. Grebennikov, R. Savinkov","doi":"10.1515/rnam-2021-0021","DOIUrl":"https://doi.org/10.1515/rnam-2021-0021","url":null,"abstract":"Abstract Pathophysiology of ischemic heart disease is a complex phenomenon determined by the interaction of multiple processes including the inflammatory, immunological, infectious, mechanical, biochemical and epigenetic ones. A predictive clinically relevant modelling of the entire trajectory of the human organism, from the initial alterations in lipid metabolism through to atherosclerotic plaque formation and finally to the pathologic state of the ischemic heart disease, is an open insufficiently explored problem. In the present review, we consider the existing mathematical frameworks which are used to describe, analyze and predict the dynamics of various processes related to cardiovascular diseases at the molecular, cellular, tissue, and holistic human organism level. The mechanistic, statistical and machine learning models are discussed in detail with special focus on the underlying assumptions and their clinical relevance. All together, they provide a solid computational platform for further expansion and tailoring for practical applications.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"255 - 266"},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45682959","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
A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations 固液两相混合物的正则化等温相场模型及其空间耗散离散化方程
IF 0.6 4区 数学
Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2021-08-01 DOI: 10.1515/rnam-2021-0017
V. Balashov
{"title":"A regularized isothermal phase-field model of two-phase solid–fluid mixture and its spatial dissipative discretization equations","authors":"V. Balashov","doi":"10.1515/rnam-2021-0017","DOIUrl":"https://doi.org/10.1515/rnam-2021-0017","url":null,"abstract":"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.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":"36 1","pages":"197 - 217"},"PeriodicalIF":0.6,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43536046","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
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