We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.
{"title":"Extracting connectivity paths in digital core images using solution of partial minimum eigenvalue problem","authors":"Serguei Yu. Maliassov, Yuri V. Vassilevski","doi":"10.1515/rnam-2023-0028","DOIUrl":"https://doi.org/10.1515/rnam-2023-0028","url":null,"abstract":"We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492818","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}
Ilya D. Tretyak, Gordey S. Goyman, Vladimir V. Shashkin
We present spatial approximation for shallow water equations on a mesh of multiple rectangular blocks with different resolution in Cartesian geometry. The approximation is based on finite-difference operators that fulfill Summation By Parts (SBP) property – a discrete analogue of integration by parts. The solution continuity conditions between mesh blocks are imposed in a weak form using Simultaneous Approximation Terms (SAT) method.We show that the resulting discrete divergence and gradient operators are anti-conjugate. The important consequences are the discrete analogues for mass and energy conservation laws along with the proof of stability for linearized equations. The numerical shallow water equations model based on the presented spatial approximation is tested using problems with meteorological context. Test results prove high-order accuracy of SBP-SAT discretization. The interfaces between mesh blocks of different resolution produce no significant noise. The local mesh refinement is shown to have positive effect on the solution both locally inside the refined region and globally in the dynamically coupled areas.
{"title":"Multiresolution approximation for shallow water equations using summation-by-parts finite differences","authors":"Ilya D. Tretyak, Gordey S. Goyman, Vladimir V. Shashkin","doi":"10.1515/rnam-2023-0030","DOIUrl":"https://doi.org/10.1515/rnam-2023-0030","url":null,"abstract":"We present spatial approximation for shallow water equations on a mesh of multiple rectangular blocks with different resolution in Cartesian geometry. The approximation is based on finite-difference operators that fulfill Summation By Parts (SBP) property – a discrete analogue of integration by parts. The solution continuity conditions between mesh blocks are imposed in a weak form using Simultaneous Approximation Terms (SAT) method.We show that the resulting discrete divergence and gradient operators are anti-conjugate. The important consequences are the discrete analogues for mass and energy conservation laws along with the proof of stability for linearized equations. The numerical shallow water equations model based on the presented spatial approximation is tested using problems with meteorological context. Test results prove high-order accuracy of SBP-SAT discretization. The interfaces between mesh blocks of different resolution produce no significant noise. The local mesh refinement is shown to have positive effect on the solution both locally inside the refined region and globally in the dynamically coupled areas.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492819","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}
Dmitry V. Kulyamin, Sergey V. Kostrykin, Pavel A. Ostanin, Valentin P. Dymnikov
The paper provides a detailed description of the numerical implementation of the transport scheme in the Earth’s ionosphere three-dimensional dynamical model of the Institute of Numerical Mathematics (INMIM). The presented version of INM-IM model takes into account the global dynamical processes of ion transport and ambipolar diffusion in the altitude range between 100 and 500 km (corresponding to F region). Based upon the splitting method the model solves the equations of ambipolar diffusion on the first split step and incorporates specifically designed advective transport scheme on the second step. The accuracy of transport scheme implementation in the model has been investigated through analytical solutions. The stability of the numerical algorithm has been demonstrated even for cases when transport velocities approaching extreme values.
{"title":"Numerical model of Earth ionosphere F region based on three-dimensional transport and ambipolar diffusion equations","authors":"Dmitry V. Kulyamin, Sergey V. Kostrykin, Pavel A. Ostanin, Valentin P. Dymnikov","doi":"10.1515/rnam-2023-0027","DOIUrl":"https://doi.org/10.1515/rnam-2023-0027","url":null,"abstract":"The paper provides a detailed description of the numerical implementation of the transport scheme in the Earth’s ionosphere three-dimensional dynamical model of the Institute of Numerical Mathematics (INMIM). The presented version of INM-IM model takes into account the global dynamical processes of ion transport and ambipolar diffusion in the altitude range between 100 and 500 km (corresponding to F region). Based upon the splitting method the model solves the equations of ambipolar diffusion on the first split step and incorporates specifically designed advective transport scheme on the second step. The accuracy of transport scheme implementation in the model has been investigated through analytical solutions. The stability of the numerical algorithm has been demonstrated even for cases when transport velocities approaching extreme values.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492814","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}
Dmitry V. Blagodatskikh, Nikolay G. Iakovlev, Evgenii M. Volodin, Andrey S. Gritsun
The present paper considers numerical properties of two different approaches to discretization of the isoneutral diffusion. The necessity of an alternative treatment of the isoneutral diffusion in a terrain-following climate ocean model as opposed to the more convenient rotated tensor formalism is studied. A new method of the approximation of the isoneutral diffusion based on a non-local computational stencil is formulated. The validity of the non-local discretization of the isoneutral diffusion operator with regard to a terrain-following vertical coordinate in the INMCM ocean model is demonstrated.
{"title":"Non-local discretization of the isoneutral diffusion operator in a terrain-following climate ocean model","authors":"Dmitry V. Blagodatskikh, Nikolay G. Iakovlev, Evgenii M. Volodin, Andrey S. Gritsun","doi":"10.1515/rnam-2023-0026","DOIUrl":"https://doi.org/10.1515/rnam-2023-0026","url":null,"abstract":"The present paper considers numerical properties of two different approaches to discretization of the isoneutral diffusion. The necessity of an alternative treatment of the isoneutral diffusion in a terrain-following climate ocean model as opposed to the more convenient rotated tensor formalism is studied. A new method of the approximation of the isoneutral diffusion based on a non-local computational stencil is formulated. The validity of the non-local discretization of the isoneutral diffusion operator with regard to a terrain-following vertical coordinate in the INMCM ocean model is demonstrated.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492815","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}
Shale rock, being a common caprock for carbon dioxide reservoirs, is subject to extensive research. One of the topics is breakthrough phenomena during injection of supercritical carbon dioxide in shale, the nature of which is still to be fully understood. In the present paper, a two-phase flow model, which may possibly be used to explain the breakthrough behaviour is examined. Capillary effects and geomechanics are included in the model, and influential model parameters are determined.
{"title":"Explaining breakthrough behaviour in shale rock: influence of capillary effects and geomechanics","authors":"Denis Anuprienko, Valentina Svitelman","doi":"10.1515/rnam-2023-0025","DOIUrl":"https://doi.org/10.1515/rnam-2023-0025","url":null,"abstract":"Shale rock, being a common caprock for carbon dioxide reservoirs, is subject to extensive research. One of the topics is breakthrough phenomena during injection of supercritical carbon dioxide in shale, the nature of which is still to be fully understood. In the present paper, a two-phase flow model, which may possibly be used to explain the breakthrough behaviour is examined. Capillary effects and geomechanics are included in the model, and influential model parameters are determined.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492817","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}
Victor P. Shutyaev, Eugene I. Parmuzin, Igor Yu. Gejadze
The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model.
{"title":"The study of the local sensitivity of functionals of the optimal solution to observational data and the heat flux input data in a variational assimilation problem for the sea thermodynamics model","authors":"Victor P. Shutyaev, Eugene I. Parmuzin, Igor Yu. Gejadze","doi":"10.1515/rnam-2023-0029","DOIUrl":"https://doi.org/10.1515/rnam-2023-0029","url":null,"abstract":"The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138492816","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}
Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov
Abstract In this work we present methods and algorithms for construction of a personalized model of coronary haemodynamics based on computed tomography images. This model provides estimations of fractional flow reserve, coronary flow reserve, and instantaneous wave-free ratio taking into account transmural perfusion ratio indices obtained from perfusion images. The presented pipeline consists of the following steps: aorta segmentation, left ventricle wall segmentation, coronary arteries segmentation, construction of 1D network of vessels, partitioning of left ventricle wall, and personalization of the model parameters. We focus on a new technique, which generates specific perfusion zones and computes transmural perfusion ratio according to the quality of available medical images with a limited number of visible terminal coronary vessels. Numerical experiments show that accurate evaluation of stenosis before precutaneous coronary intervention should take into account both fractional flow reserve indices and myocardial perfusion, as well as other indices, in order to avoid misdiagnosis. The presented model provides better understanding of the background of clinical recommendations for possible surgical treatment of a stenosed coronary artery.
{"title":"Myocardial perfusion segmentation and partitioning methods in personalized models of coronary blood flow","authors":"Alexander A. Danilov, Timur M. Gamilov, Fuyou Liang, Alina A. Rebrova, Petr Sh. Chomakhidze, Philipp Yu. Kopylov, Yan R. Bravyy, Sergey S. Simakov","doi":"10.1515/rnam-2023-0022","DOIUrl":"https://doi.org/10.1515/rnam-2023-0022","url":null,"abstract":"Abstract In this work we present methods and algorithms for construction of a personalized model of coronary haemodynamics based on computed tomography images. This model provides estimations of fractional flow reserve, coronary flow reserve, and instantaneous wave-free ratio taking into account transmural perfusion ratio indices obtained from perfusion images. The presented pipeline consists of the following steps: aorta segmentation, left ventricle wall segmentation, coronary arteries segmentation, construction of 1D network of vessels, partitioning of left ventricle wall, and personalization of the model parameters. We focus on a new technique, which generates specific perfusion zones and computes transmural perfusion ratio according to the quality of available medical images with a limited number of visible terminal coronary vessels. Numerical experiments show that accurate evaluation of stenosis before precutaneous coronary intervention should take into account both fractional flow reserve indices and myocardial perfusion, as well as other indices, in order to avoid misdiagnosis. The presented model provides better understanding of the background of clinical recommendations for possible surgical treatment of a stenosed coronary artery.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198951","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}
Pub Date : 2023-10-01DOI: 10.1515/rnam-2023-frontmatter5
{"title":"Frontmatter","authors":"","doi":"10.1515/rnam-2023-frontmatter5","DOIUrl":"https://doi.org/10.1515/rnam-2023-frontmatter5","url":null,"abstract":"","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198954","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}
Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov
Abstract The immune system is a complex distributed system consisting of cells, which circulate through the body, communicate and turnover in response to antigenic perturbations. We discuss new approaches to modelling the functioning of the immune system of humans and experimental animals with a focus on its ‘complexity’. Emerging mathematical and computer models are reviewed to describe the immune system diversity, the cell/cytokine network communication structures, hierarchical regulation, and evolutionary dynamics of immune repertoires.
{"title":"Multiphysics modelling of immune processes using distributed parameter systems","authors":"Gennady A. Bocharov, Dmitry S. Grebennikov, Rostislav S. Savinkov","doi":"10.1515/rnam-2023-0021","DOIUrl":"https://doi.org/10.1515/rnam-2023-0021","url":null,"abstract":"Abstract The immune system is a complex distributed system consisting of cells, which circulate through the body, communicate and turnover in response to antigenic perturbations. We discuss new approaches to modelling the functioning of the immune system of humans and experimental animals with a focus on its ‘complexity’. Emerging mathematical and computer models are reviewed to describe the immune system diversity, the cell/cytokine network communication structures, hierarchical regulation, and evolutionary dynamics of immune repertoires.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198952","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}
Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.
{"title":"One-dimensional haemodynamic model of a vascular network with fractional-order viscoelasticity","authors":"Ruslan Yanbarisov, Timur Gamilov","doi":"10.1515/rnam-2023-0024","DOIUrl":"https://doi.org/10.1515/rnam-2023-0024","url":null,"abstract":"Abstract We propose a computational framework for a one-dimensional haemodynamic model with the arterial walls described by the fractional-order viscoelastic material constitutive law. This framework is used to compare blood flow characteristics for simulations with elastic and fractional-order viscoelastic walls. We use three well-established benchmark tests: a single pulse wave in a long vessel, flow in a 37-segment network of elastic tubes, and flow in anatomically detailed arterial network consisting of 61 arterial segments. All results for elastic model are in a good agreement with analytical solutions, in vitro data and other well-established approaches. Fractional-order model demonstrates noticeable differences in pulse wave propagation speed and minor differences in pressure and flow profiles. Differences in profiles are negligible in major vessels, but more profound in vessels beyond the third or fourth generation.","PeriodicalId":49585,"journal":{"name":"Russian Journal of Numerical Analysis and Mathematical Modelling","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198953","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}
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