Application of nonlinearity continuation method to numerical solution of steady-state groundwater... more Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume discretization of steady-state Richards equation, a series of problems with increasing nonlinearity are solved using the Newton method. This approach is compared to pseudo-transient method on several test cases, including real site problems and involving parallel computations.
Communications in computer and information science, Dec 31, 2018
Flow of variable density solution in unconfined conditions and transport in dual-porosity media m... more Flow of variable density solution in unconfined conditions and transport in dual-porosity media mathematical model is introduced. We show the application of the model to a real object which is a polygon of deep well liquid radioactive waste injection. Several assumptions are justified to simplify the model and it is discretized. The model is aimed at assessment of the role of density changes on the contaminant propagation dynamics within the polygon. The method of parallelization is described and the results of numerical experiments are presented herein.
Vyčislitelʹnye metody i programmirovanie, Dec 18, 2015
Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionucli... more Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionuclide transport problems are discussed. The first one is a triangular-prismatic generator with the ability of cell degeneration; the second one is the polyhedral octree mesh generator implementing the cut-cell technology. These generators allow the user to automatically create conformal polyhedral adaptive grids in three-dimensional geological domains with consideration of complex boundaries, top and bottom geological layer surfaces, pinchouts, and geological heterogeneities.
Vyčislitelʹnye metody i programmirovanie, Dec 18, 2018
The structure, functionality and parallel computation organization of the computational code GeRa... more The structure, functionality and parallel computation organization of the computational code GeRa designed for hydrogeological modeling are considered. The principles of multiprocessor task launching on a remote cluster directly from the GeRa graphical user interface are described. The results of parallel computations for three representative models are presented and analyzed from the standpoint of parallel efficiency.
This paper provides a brief review of the existing models in the Russian Federation to forecast r... more This paper provides a brief review of the existing models in the Russian Federation to forecast radionuclide migration in the geological environment, as well as experience of the Nuclear Safety Institute in this field. The prospective codes are considered, which are aimed at describing three-dimensional groundwater flow and advective-diffusive transport of radioactive substances taking into account for sorption and decay. The discretizations to deal with unstructured mixed cell type meshes. The main prospective numerical techniques are novel finite volume methods, transport schemes with low numerical diffusion and operator-splitting schemes.
This article is devoted to the problem of thermal convection in porous media with volumetric heat... more This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in practice of radioactive waste (RW) disposal safety assessment. In the first section a brief overview of widespread hydrogeological codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to solve thermal problems is done. We point out the lack of heat generation caused by radioactive decay model in these programs. The GeRa numerical code developed by the authors is presented. In the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is implemented in GeRa. The model describes these processes in saturated porous media and takes into account radioactive decay, sorption on the rock, the dependences of density and viscosity on temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model includes heat transport by convecti...
Geochemical simulation of strontium sorption was considered within the framework of studying the ... more Geochemical simulation of strontium sorption was considered within the framework of studying the radionuclide geomigration. A chemical model describing the interaction in the solution–surrounding rock system under the experimental conditions was constructed on the basis of the experimental data. The influence of the geochemical simulation detailedness on the calculation results was evaluated in numerical experiments performed using the GeRa code developed by the authors. Three sorption models were used: traditional model of linear sorption with the tabulated value of Kd; new model with variable Kd, measured experimentally and functionally depending on the NaNO3 concentration; model with direct calculation of chemical interactions, in which the sorption is considered within the framework of the ion-exchange model.
Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), 2015
Рассматриваются два сеточных генератора, внедренных в программный комплекс GeRa, предназначенный ... more Рассматриваются два сеточных генератора, внедренных в программный комплекс GeRa, предназначенный для решения задач геофильтрации и геомиграции радионуклидов. Это треугольно-призматический генератор с возможностью вырождения ячеек и генератор многогранных сеток с измельчением на основе восьмеричного дерева и возможностями скалывания ячеек. Генераторы позволяют автоматически строить конформные многогранные адаптивные сетки в трехмерных геологических областях с учетом сложной конфигурации внешних границ, кровель и подошв геологических пластов, выклинивания слоев и геологических неоднородностей. Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionuclide transport problems are discussed. The first one is a triangular-prismatic generator with the ability of cell degeneration; the second one is the polyhedral octree mesh generator implementing the cut-cell technology. These generators allow the user to automatically create conformal polyhedral adapt...
Russian Journal of Numerical Analysis and Mathematical Modelling
A particle tracking method based on face fluxes data calculated using finite volume methods is de... more A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation are provided. Performance and convergence of the method are demonstrated on a set of reference problems.
This article discusses a three-dimensional groundwater flow model of a deep disposal facility at ... more This article discusses a three-dimensional groundwater flow model of a deep disposal facility at Severny test site. The three-dimensional model is a part of the certified software GEOPOLIS, based on the hydrogeological code GeRa (Geomigration of Radionuclides) serving as the calculation engine. This study describes the hydrogeological patterning of the groundwater flow model, as well as the results of calibration and verification of the model water heads with respect to the data of monitoring for more than 40 years of the deep repository exploitation. The article begins with a brief overview of the previously developed hydrogeological models of this object and continues with a description of the geological structure of the territory, and with a substantiation of the boundaries and parameters of the model. The results of groundwater flow modeling, model calibration, verification and estimation of discrepancy between the model results and monitoring data are shown. The comparison of t...
The paper analyzes modern trends in the development and use of software systems for three-dimensi... more The paper analyzes modern trends in the development and use of software systems for three-dimensional hydrogeological modeling. It provides an analytical overview of most recent and widely used software products, their development process, the implemented models and the numerical methods applied. The study specifies a range of typical tasks addressed by Russian nuclear industry requiring the development of numerical geofiltration and geomigration models. To demonstrate the use of modern computational technologies, studied was the case involving calculations in the GeRa software package performed for LRW DDF. The paper identifies the trends for further software evolution taking into account the Russian needs in the development of near-surface and deep RW disposal facilities, decommissioning, as well as the accumulated experience in the operation of RW storage facilities and global trends in the code development.
The article evaluates the impact of a “buried wall” barrier on the long-term safety during the lo... more The article evaluates the impact of a “buried wall” barrier on the long-term safety during the long-term storage1 or in-situ disposal of nuclear legacy facilities, in particular, industrial reservoirs, as well as during the development of near-surface disposal facilities for radioactive waste (RWDF). For assessment purposes, filtration and mass transfer processes have been numerically modelled in the GeRa code based on a case study of a reference near-surface facility. The study explores in which way the available covering screen affects the dynamics of contaminant spread. It evaluates the sensitivity of the results to the dispersion parameter commonly characterized by a high degree of uncertainty.
Parallel Finite Volume Computation on General Meshes, 2020
The chapter is devoted to application of the monotone FM methods in reservoir simulation. We will... more The chapter is devoted to application of the monotone FM methods in reservoir simulation. We will consider single-phase and multi-phase black-oil models, flows in fractured media, and well-driven flows. The black-oil model is the set of PDEs that describe subsurface flow during the oil and gas recovery from natural subsurface reservoirs. The numerical modeling is the primary decision-making tool for well drilling and management. Geological surveys, core analysis, ultrasound reconnaissance, and laboratory tests are mandatory steps preceding the reservoir simulation. Reservoir simulation implies multiple numerical tests with various scenarios to coin out the best strategy for management of a particular reservoir. Multiple runs of the simulator require its computational efficiency and physically correct results. Monotone FV schemes facilitate achieving these goals.
This article is devoted to the problem of thermal convection in porous media with volumetric heat... more This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in practice of radioactive waste (RW) disposal safety assessment. In the first section a brief overview of widespread hydrogeological codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to solve thermal problems is done. We point out the lack of heat generation caused by radioactive decay model in these programs. The GeRa numerical code developed by the authors is presented. In the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is implemented in GeRa. The model describes these processes in saturated porous media and takes into account radioactive decay, sorption on the rock, the dependences of density and viscosity on temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model includes heat transport by convection and conduction-thermal
The hydrogeological modeling code GeRa is based on INMOST software platform, which operates with ... more The hydrogeological modeling code GeRa is based on INMOST software platform, which operates with distributed mesh data and allows to assemble and solve the system of linear equations. The set of groundwater flow models with filtration, transport, and chemical processes are considered. The comparison of parallel efficiency for different linear solvers in the INMOST framework is performed. The analysis of scalability of GeRa code on different computer platforms from multicore laptop to Lomonosov supercomputer is presented.
Integrated Numerical Modeling Object-oriented Supercomputing Technologies (INMOST) is an open-sou... more Integrated Numerical Modeling Object-oriented Supercomputing Technologies (INMOST) is an open-source, flexible, and efficient numerical modeling framework that provides to application developers all the tools required for fast development of parallel multi-physics models. The users of INMOST avoid designing and implementing their own mesh data structures. They enjoy low-level infrastructure for reading, writing, creating, manipulating, and partitioning distributed unstructured general meshes. FV discretizations of systems of PDEs may lead to systems of nonlinear algebraic equations. The nonlinear algebraic equations are solved iteratively. On each nonlinear iteration, a sparse linear system corresponding to the nonlinear residual is assembled and solved. INMOST provides software tools that cover the complete process for parallel assembly and solution of linear systems arising in the iterative solution of nonlinear systems. To simplify the solution, the user can use INMOST tool for a...
Application of nonlinearity continuation method to numerical solution of steady-state groundwater... more Application of nonlinearity continuation method to numerical solution of steady-state groundwater flow in variably saturated conditions is presented. In order to solve the system of nonlinear equations obtained by finite volume discretization of steady-state Richards equation, a series of problems with increasing nonlinearity are solved using the Newton method. This approach is compared to pseudo-transient method on several test cases, including real site problems and involving parallel computations.
Communications in computer and information science, Dec 31, 2018
Flow of variable density solution in unconfined conditions and transport in dual-porosity media m... more Flow of variable density solution in unconfined conditions and transport in dual-porosity media mathematical model is introduced. We show the application of the model to a real object which is a polygon of deep well liquid radioactive waste injection. Several assumptions are justified to simplify the model and it is discretized. The model is aimed at assessment of the role of density changes on the contaminant propagation dynamics within the polygon. The method of parallelization is described and the results of numerical experiments are presented herein.
Vyčislitelʹnye metody i programmirovanie, Dec 18, 2015
Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionucli... more Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionuclide transport problems are discussed. The first one is a triangular-prismatic generator with the ability of cell degeneration; the second one is the polyhedral octree mesh generator implementing the cut-cell technology. These generators allow the user to automatically create conformal polyhedral adaptive grids in three-dimensional geological domains with consideration of complex boundaries, top and bottom geological layer surfaces, pinchouts, and geological heterogeneities.
Vyčislitelʹnye metody i programmirovanie, Dec 18, 2018
The structure, functionality and parallel computation organization of the computational code GeRa... more The structure, functionality and parallel computation organization of the computational code GeRa designed for hydrogeological modeling are considered. The principles of multiprocessor task launching on a remote cluster directly from the GeRa graphical user interface are described. The results of parallel computations for three representative models are presented and analyzed from the standpoint of parallel efficiency.
This paper provides a brief review of the existing models in the Russian Federation to forecast r... more This paper provides a brief review of the existing models in the Russian Federation to forecast radionuclide migration in the geological environment, as well as experience of the Nuclear Safety Institute in this field. The prospective codes are considered, which are aimed at describing three-dimensional groundwater flow and advective-diffusive transport of radioactive substances taking into account for sorption and decay. The discretizations to deal with unstructured mixed cell type meshes. The main prospective numerical techniques are novel finite volume methods, transport schemes with low numerical diffusion and operator-splitting schemes.
This article is devoted to the problem of thermal convection in porous media with volumetric heat... more This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in practice of radioactive waste (RW) disposal safety assessment. In the first section a brief overview of widespread hydrogeological codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to solve thermal problems is done. We point out the lack of heat generation caused by radioactive decay model in these programs. The GeRa numerical code developed by the authors is presented. In the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is implemented in GeRa. The model describes these processes in saturated porous media and takes into account radioactive decay, sorption on the rock, the dependences of density and viscosity on temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model includes heat transport by convecti...
Geochemical simulation of strontium sorption was considered within the framework of studying the ... more Geochemical simulation of strontium sorption was considered within the framework of studying the radionuclide geomigration. A chemical model describing the interaction in the solution–surrounding rock system under the experimental conditions was constructed on the basis of the experimental data. The influence of the geochemical simulation detailedness on the calculation results was evaluated in numerical experiments performed using the GeRa code developed by the authors. Three sorption models were used: traditional model of linear sorption with the tabulated value of Kd; new model with variable Kd, measured experimentally and functionally depending on the NaNO3 concentration; model with direct calculation of chemical interactions, in which the sorption is considered within the framework of the ion-exchange model.
Numerical Methods and Programming (Vychislitel'nye Metody i Programmirovanie), 2015
Рассматриваются два сеточных генератора, внедренных в программный комплекс GeRa, предназначенный ... more Рассматриваются два сеточных генератора, внедренных в программный комплекс GeRa, предназначенный для решения задач геофильтрации и геомиграции радионуклидов. Это треугольно-призматический генератор с возможностью вырождения ячеек и генератор многогранных сеток с измельчением на основе восьмеричного дерева и возможностями скалывания ячеек. Генераторы позволяют автоматически строить конформные многогранные адаптивные сетки в трехмерных геологических областях с учетом сложной конфигурации внешних границ, кровель и подошв геологических пластов, выклинивания слоев и геологических неоднородностей. Two mesh generators embedded in the GeRa code for the solution of groundwater flow and radionuclide transport problems are discussed. The first one is a triangular-prismatic generator with the ability of cell degeneration; the second one is the polyhedral octree mesh generator implementing the cut-cell technology. These generators allow the user to automatically create conformal polyhedral adapt...
Russian Journal of Numerical Analysis and Mathematical Modelling
A particle tracking method based on face fluxes data calculated using finite volume methods is de... more A particle tracking method based on face fluxes data calculated using finite volume methods is developed for unstructured three-dimensional polyhedral grids. The flow velocity field reconstruction on grid cells using a mixed finite element method is proposed. Cases of sinks and sources in cells as well as different cell partitionings are considered. Algorithms for streamlines and time of flight calculation are provided. Performance and convergence of the method are demonstrated on a set of reference problems.
This article discusses a three-dimensional groundwater flow model of a deep disposal facility at ... more This article discusses a three-dimensional groundwater flow model of a deep disposal facility at Severny test site. The three-dimensional model is a part of the certified software GEOPOLIS, based on the hydrogeological code GeRa (Geomigration of Radionuclides) serving as the calculation engine. This study describes the hydrogeological patterning of the groundwater flow model, as well as the results of calibration and verification of the model water heads with respect to the data of monitoring for more than 40 years of the deep repository exploitation. The article begins with a brief overview of the previously developed hydrogeological models of this object and continues with a description of the geological structure of the territory, and with a substantiation of the boundaries and parameters of the model. The results of groundwater flow modeling, model calibration, verification and estimation of discrepancy between the model results and monitoring data are shown. The comparison of t...
The paper analyzes modern trends in the development and use of software systems for three-dimensi... more The paper analyzes modern trends in the development and use of software systems for three-dimensional hydrogeological modeling. It provides an analytical overview of most recent and widely used software products, their development process, the implemented models and the numerical methods applied. The study specifies a range of typical tasks addressed by Russian nuclear industry requiring the development of numerical geofiltration and geomigration models. To demonstrate the use of modern computational technologies, studied was the case involving calculations in the GeRa software package performed for LRW DDF. The paper identifies the trends for further software evolution taking into account the Russian needs in the development of near-surface and deep RW disposal facilities, decommissioning, as well as the accumulated experience in the operation of RW storage facilities and global trends in the code development.
The article evaluates the impact of a “buried wall” barrier on the long-term safety during the lo... more The article evaluates the impact of a “buried wall” barrier on the long-term safety during the long-term storage1 or in-situ disposal of nuclear legacy facilities, in particular, industrial reservoirs, as well as during the development of near-surface disposal facilities for radioactive waste (RWDF). For assessment purposes, filtration and mass transfer processes have been numerically modelled in the GeRa code based on a case study of a reference near-surface facility. The study explores in which way the available covering screen affects the dynamics of contaminant spread. It evaluates the sensitivity of the results to the dispersion parameter commonly characterized by a high degree of uncertainty.
Parallel Finite Volume Computation on General Meshes, 2020
The chapter is devoted to application of the monotone FM methods in reservoir simulation. We will... more The chapter is devoted to application of the monotone FM methods in reservoir simulation. We will consider single-phase and multi-phase black-oil models, flows in fractured media, and well-driven flows. The black-oil model is the set of PDEs that describe subsurface flow during the oil and gas recovery from natural subsurface reservoirs. The numerical modeling is the primary decision-making tool for well drilling and management. Geological surveys, core analysis, ultrasound reconnaissance, and laboratory tests are mandatory steps preceding the reservoir simulation. Reservoir simulation implies multiple numerical tests with various scenarios to coin out the best strategy for management of a particular reservoir. Multiple runs of the simulator require its computational efficiency and physically correct results. Monotone FV schemes facilitate achieving these goals.
This article is devoted to the problem of thermal convection in porous media with volumetric heat... more This article is devoted to the problem of thermal convection in porous media with volumetric heat generation modelling, arising in practice of radioactive waste (RW) disposal safety assessment. In the first section a brief overview of widespread hydrogeological codes (FEFLOW, SUTRA, SEAWAT, TOUGH2) featuring the ability to solve thermal problems is done. We point out the lack of heat generation caused by radioactive decay model in these programs. The GeRa numerical code developed by the authors is presented. In the second section we consider the mathematical model of coupled groundwater flow, solute and heat transport, which is implemented in GeRa. The model describes these processes in saturated porous media and takes into account radioactive decay, sorption on the rock, the dependences of density and viscosity on temperature. The heat transport equation is written assuming thermal equilibrium between the fluid and the rock. The model includes heat transport by convection and conduction-thermal
The hydrogeological modeling code GeRa is based on INMOST software platform, which operates with ... more The hydrogeological modeling code GeRa is based on INMOST software platform, which operates with distributed mesh data and allows to assemble and solve the system of linear equations. The set of groundwater flow models with filtration, transport, and chemical processes are considered. The comparison of parallel efficiency for different linear solvers in the INMOST framework is performed. The analysis of scalability of GeRa code on different computer platforms from multicore laptop to Lomonosov supercomputer is presented.
Integrated Numerical Modeling Object-oriented Supercomputing Technologies (INMOST) is an open-sou... more Integrated Numerical Modeling Object-oriented Supercomputing Technologies (INMOST) is an open-source, flexible, and efficient numerical modeling framework that provides to application developers all the tools required for fast development of parallel multi-physics models. The users of INMOST avoid designing and implementing their own mesh data structures. They enjoy low-level infrastructure for reading, writing, creating, manipulating, and partitioning distributed unstructured general meshes. FV discretizations of systems of PDEs may lead to systems of nonlinear algebraic equations. The nonlinear algebraic equations are solved iteratively. On each nonlinear iteration, a sparse linear system corresponding to the nonlinear residual is assembled and solved. INMOST provides software tools that cover the complete process for parallel assembly and solution of linear systems arising in the iterative solution of nonlinear systems. To simplify the solution, the user can use INMOST tool for a...
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Papers by Ivan Kapyrin