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G Verdu - One of the best experts on this subject based on the ideXlab platform.
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modal methods for the Neutron Diffusion Equation using different spatial modes
Progress in Nuclear Energy, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract The behaviour of the Neutrons inside a nuclear reactor core can be modelled by using the time dependent Neutron Diffusion Equation. Different time schemes have been used to integrate this Equation. One possibility is to use a modal method, which is based on the expansion of the Neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. In this work, the λ , the α and the γ -modes have been used to develop different modal kinetics Equations, using a high order finite element method for the spatial discretization of the Neutron Diffusion Equation. The performance of the different modal kinetic Equations has been tested and compared using two 3D transient benchmark problems.
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a matrix free eigenvalue solver for the multigroup Neutron Diffusion Equation
International Conference on Computational Science, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:The stationary Neutron transport Equation describes the Neutron population and thus, the generated heat, inside a nuclear reactor core. Obtaining the solution of this Equation requires to solve a generalized eigenvalue problem efficiently. The majority of the eigenvalue solvers use the factorization of the system matrices to construct preconditioners, such as the ILU decomposition or the ICC decomposition, to speed up the convergence of the methods. The storage of the involved matrices and incomplete factorization demands high quantities of computational memory although a the sparse format is used. This makes the computational memory the limiting factor for this kind of calculations in some personal computers. In this work, we propose a matrix-free preconditioned eigenvalue solver that does not need to have the matrices allocated in memory explicitly. This method is based on the block inverse-free preconditioned Arnoldi method (BIFPAM) with the innovation that uses a preconditioner that is applied from matrix-vector operations. As well as reducing enormously the computational memory, this methodology removes the time to assembly the sparse matrices involved in the system. A two-dimensional and three-dimensional benchmarks are used to study the performance of the methodology proposed.
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block preconditioning matrices for the newton method to compute the dominant λ modes associated with the Neutron Diffusion Equation
Mathematical & Computational Applications, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, Luca Bergamaschi, Angeles Martinez, G VerduAbstract:In nuclear engineering, the λ -modes associated with the Neutron Diffusion Equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied.
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calculation of multiple eigenvalues of the Neutron Diffusion Equation discretized with a parallelized finite volume method
Progress in Nuclear Energy, 2018Co-Authors: Alvaro Bernal, Jose E Roman, R Miro, G VerduAbstract:Abstract The spatial distribution of the Neutron flux within the core of nuclear reactors is a key factor in nuclear safety. The easiest and fastest way to determine it is by solving the eigenvalue problem of the Neutron Diffusion Equation, which only contains spatial derivatives. The approximation of these derivatives is performed by discretizing the geometry and using numerical methods. In this work, the authors used a finite volume method based on a polynomial expansion of the Neutron flux. Once these terms are discretized, a set of matrix Equations is obtained, which constitutes the eigenvalue problem. A very effective class of methods for the solution of eigenvalue problems are those based on projection onto a low-dimensional subspace, such as Krylov subspaces. Thus, the SLEPc library was used for solving the eigenvalue problem by means of the Krylov-Schur method, which also uses projection methods of PETSc for solving linear systems. This work includes a complete sensitivity analysis of different issues: mesh, polynomial terms, linear systems solvers and parallelization.
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spatial modes for the Neutron Diffusion Equation and their computation
Annals of Nuclear Energy, 2017Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract Different spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. These modes have been successfully used for the analysis of nuclear reactor characteristics. In this work, these modes are studied using a high order finite element method to discretize the Equations and also different methods to solve the resulting algebraic eigenproblems, are compared. Particularly, Krylov subspace methods and block-Newton methods have been studied. The performance of these methods has been tested in several 3D benchmark problems: a homogeneous reactor and several configurations of NEACRP reactor.
D Ginestar - One of the best experts on this subject based on the ideXlab platform.
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modal methods for the Neutron Diffusion Equation using different spatial modes
Progress in Nuclear Energy, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract The behaviour of the Neutrons inside a nuclear reactor core can be modelled by using the time dependent Neutron Diffusion Equation. Different time schemes have been used to integrate this Equation. One possibility is to use a modal method, which is based on the expansion of the Neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. In this work, the λ , the α and the γ -modes have been used to develop different modal kinetics Equations, using a high order finite element method for the spatial discretization of the Neutron Diffusion Equation. The performance of the different modal kinetic Equations has been tested and compared using two 3D transient benchmark problems.
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a matrix free eigenvalue solver for the multigroup Neutron Diffusion Equation
International Conference on Computational Science, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:The stationary Neutron transport Equation describes the Neutron population and thus, the generated heat, inside a nuclear reactor core. Obtaining the solution of this Equation requires to solve a generalized eigenvalue problem efficiently. The majority of the eigenvalue solvers use the factorization of the system matrices to construct preconditioners, such as the ILU decomposition or the ICC decomposition, to speed up the convergence of the methods. The storage of the involved matrices and incomplete factorization demands high quantities of computational memory although a the sparse format is used. This makes the computational memory the limiting factor for this kind of calculations in some personal computers. In this work, we propose a matrix-free preconditioned eigenvalue solver that does not need to have the matrices allocated in memory explicitly. This method is based on the block inverse-free preconditioned Arnoldi method (BIFPAM) with the innovation that uses a preconditioner that is applied from matrix-vector operations. As well as reducing enormously the computational memory, this methodology removes the time to assembly the sparse matrices involved in the system. A two-dimensional and three-dimensional benchmarks are used to study the performance of the methodology proposed.
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block preconditioning matrices for the newton method to compute the dominant λ modes associated with the Neutron Diffusion Equation
Mathematical & Computational Applications, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, Luca Bergamaschi, Angeles Martinez, G VerduAbstract:In nuclear engineering, the λ -modes associated with the Neutron Diffusion Equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied.
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spatial modes for the Neutron Diffusion Equation and their computation
Annals of Nuclear Energy, 2017Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract Different spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. These modes have been successfully used for the analysis of nuclear reactor characteristics. In this work, these modes are studied using a high order finite element method to discretize the Equations and also different methods to solve the resulting algebraic eigenproblems, are compared. Particularly, Krylov subspace methods and block-Newton methods have been studied. The performance of these methods has been tested in several 3D benchmark problems: a homogeneous reactor and several configurations of NEACRP reactor.
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multilevel method to compute the lambda modes of the Neutron Diffusion Equation
Applied Mathematics and Nonlinear Sciences, 2017Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Determination of the reactor kinetic characteristics is very important for the design and development of a new reactor system. In this sense, the computation of lambda modes associated to a nuclear power reactor has interest since these modes can be used to analyze the reactor criticality and to develop modal methods to analyze transient situations in the reactor. In this paper, the lambda problem has been discretized using a high order finite element method to obtain a generalized algebraic eigenvalue problem. A multilevel method is proposed to solve this generalized eigenvalue problem combining a hierarchy of meshes with a Modified Block Newton method. The Krylov-Schur method is used to compare the efficiency of the multilevel method solving several benchmark problems.
Alvaro Bernal - One of the best experts on this subject based on the ideXlab platform.
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calculation of multiple eigenvalues of the Neutron Diffusion Equation discretized with a parallelized finite volume method
Progress in Nuclear Energy, 2018Co-Authors: Alvaro Bernal, Jose E Roman, R Miro, G VerduAbstract:Abstract The spatial distribution of the Neutron flux within the core of nuclear reactors is a key factor in nuclear safety. The easiest and fastest way to determine it is by solving the eigenvalue problem of the Neutron Diffusion Equation, which only contains spatial derivatives. The approximation of these derivatives is performed by discretizing the geometry and using numerical methods. In this work, the authors used a finite volume method based on a polynomial expansion of the Neutron flux. Once these terms are discretized, a set of matrix Equations is obtained, which constitutes the eigenvalue problem. A very effective class of methods for the solution of eigenvalue problems are those based on projection onto a low-dimensional subspace, such as Krylov subspaces. Thus, the SLEPc library was used for solving the eigenvalue problem by means of the Krylov-Schur method, which also uses projection methods of PETSc for solving linear systems. This work includes a complete sensitivity analysis of different issues: mesh, polynomial terms, linear systems solvers and parallelization.
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a krylov schur solution of the eigenvalue problem for the Neutron Diffusion Equation discretized with the raviart thomas method
Journal of Nuclear Science and Technology, 2017Co-Authors: Alvaro Bernal, Alain Hebert, Jose E Roman, R Miro, G VerduAbstract:ABSTRACTMixed-dual formulations of the finite element method were successfully applied to the Neutron Diffusion Equation, such as the Raviart–Thomas method in Cartesian geometry and the Raviart–Thomas–Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov–Schur. In this work, a Krylov–Schur method has been applied to the Neutron Diffusion Equation, discretized with the Raviart–Thomas and Raviart–Thomas–Schneider methods.
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A Krylov–Schur solution of the eigenvalue problem for the Neutron Diffusion Equation discretized with the Raviart–Thomas method
Journal of Nuclear Science and Technology, 2017Co-Authors: Alvaro Bernal, Alain Hebert, Jose E Roman, R Miro, Gumersindo VerdúAbstract:ABSTRACTMixed-dual formulations of the finite element method were successfully applied to the Neutron Diffusion Equation, such as the Raviart–Thomas method in Cartesian geometry and the Raviart–Thomas–Schneider in hexagonal geometry. Both methods obtain system matrices which are suitable for solving the eigenvalue problem with the preconditioned power method. This method is very fast and optimized, but only for the calculation of the fundamental mode. However, the determination of non-fundamental modes is important for modal analysis, instabilities, and fluctuations of nuclear reactors. So, effective and fast methods are required for solving eigenvalue problems. The most effective methods are those based on Krylov subspaces projection combined with restart, such as Krylov–Schur. In this work, a Krylov–Schur method has been applied to the Neutron Diffusion Equation, discretized with the Raviart–Thomas and Raviart–Thomas–Schneider methods.
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assembly discontinuity factors for the Neutron Diffusion Equation discretized with the finite volume method application to bwr
Annals of Nuclear Energy, 2016Co-Authors: Alvaro Bernal, Jose E Roman, R Miro, G VerduAbstract:Abstract The Neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential Equation. In steady state conditions, the time derivative terms are zero and this Equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.
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development of a finite volume inter cell polynomial expansion method for the Neutron Diffusion Equation
Journal of Nuclear Science and Technology, 2016Co-Authors: Alvaro Bernal, D Ginestar, Jose E Roman, R Miro, G VerduAbstract:Heterogeneous nuclear reactors require numerical methods to solve the Neutron Diffusion Equation (NDE) to obtain the Neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional Equations at the inner faces of two adjacent cells: Neutron flux and current continuity, which imply an excess of Equations. The finite volume method (FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically used in the transport Equations due to the conservation of the transported quantity within the volume. However, the gradient and face-averaged values in the FVM are typically calculated as a function of the cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the Neutron current condition could not be accomplished. Therefore, a polynomial expansion of the Neutron flux is developed in each cell for assuring the accomplishment of the flux and cur...
Antoni Vidalferrandiz - One of the best experts on this subject based on the ideXlab platform.
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modal methods for the Neutron Diffusion Equation using different spatial modes
Progress in Nuclear Energy, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract The behaviour of the Neutrons inside a nuclear reactor core can be modelled by using the time dependent Neutron Diffusion Equation. Different time schemes have been used to integrate this Equation. One possibility is to use a modal method, which is based on the expansion of the Neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. In this work, the λ , the α and the γ -modes have been used to develop different modal kinetics Equations, using a high order finite element method for the spatial discretization of the Neutron Diffusion Equation. The performance of the different modal kinetic Equations has been tested and compared using two 3D transient benchmark problems.
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a matrix free eigenvalue solver for the multigroup Neutron Diffusion Equation
International Conference on Computational Science, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:The stationary Neutron transport Equation describes the Neutron population and thus, the generated heat, inside a nuclear reactor core. Obtaining the solution of this Equation requires to solve a generalized eigenvalue problem efficiently. The majority of the eigenvalue solvers use the factorization of the system matrices to construct preconditioners, such as the ILU decomposition or the ICC decomposition, to speed up the convergence of the methods. The storage of the involved matrices and incomplete factorization demands high quantities of computational memory although a the sparse format is used. This makes the computational memory the limiting factor for this kind of calculations in some personal computers. In this work, we propose a matrix-free preconditioned eigenvalue solver that does not need to have the matrices allocated in memory explicitly. This method is based on the block inverse-free preconditioned Arnoldi method (BIFPAM) with the innovation that uses a preconditioner that is applied from matrix-vector operations. As well as reducing enormously the computational memory, this methodology removes the time to assembly the sparse matrices involved in the system. A two-dimensional and three-dimensional benchmarks are used to study the performance of the methodology proposed.
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block preconditioning matrices for the newton method to compute the dominant λ modes associated with the Neutron Diffusion Equation
Mathematical & Computational Applications, 2019Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, Luca Bergamaschi, Angeles Martinez, G VerduAbstract:In nuclear engineering, the λ -modes associated with the Neutron Diffusion Equation are applied to study the criticality of reactors and to develop modal methods for the transient analysis. The differential eigenvalue problem that needs to be solved is discretized using a finite element method, obtaining a generalized algebraic eigenvalue problem whose associated matrices are large and sparse. Then, efficient methods are needed to solve this problem. In this work, we used a block generalized Newton method implemented with a matrix-free technique that does not store all matrices explicitly. This technique reduces mainly the computational memory and, in some cases, when the assembly of the matrices is an expensive task, the computational time. The main problem is that the block Newton method requires solving linear systems, which need to be preconditioned. The construction of preconditioners such as ILU or ICC based on a fully-assembled matrix is not efficient in terms of the memory with the matrix-free implementation. As an alternative, several block preconditioners are studied that only save a few block matrices in comparison with the full problem. To test the performance of these methodologies, different reactor problems are studied.
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spatial modes for the Neutron Diffusion Equation and their computation
Annals of Nuclear Energy, 2017Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Abstract Different spatial modes can be defined for the Neutron Diffusion Equation such as the λ , α and γ -modes. These modes have been successfully used for the analysis of nuclear reactor characteristics. In this work, these modes are studied using a high order finite element method to discretize the Equations and also different methods to solve the resulting algebraic eigenproblems, are compared. Particularly, Krylov subspace methods and block-Newton methods have been studied. The performance of these methods has been tested in several 3D benchmark problems: a homogeneous reactor and several configurations of NEACRP reactor.
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multilevel method to compute the lambda modes of the Neutron Diffusion Equation
Applied Mathematics and Nonlinear Sciences, 2017Co-Authors: Amanda Carreno, D Ginestar, Antoni Vidalferrandiz, G VerduAbstract:Determination of the reactor kinetic characteristics is very important for the design and development of a new reactor system. In this sense, the computation of lambda modes associated to a nuclear power reactor has interest since these modes can be used to analyze the reactor criticality and to develop modal methods to analyze transient situations in the reactor. In this paper, the lambda problem has been discretized using a high order finite element method to obtain a generalized algebraic eigenvalue problem. A multilevel method is proposed to solve this generalized eigenvalue problem combining a hierarchy of meshes with a Modified Block Newton method. The Krylov-Schur method is used to compare the efficiency of the multilevel method solving several benchmark problems.
R Miro - One of the best experts on this subject based on the ideXlab platform.
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calculation of multiple eigenvalues of the Neutron Diffusion Equation discretized with a parallelized finite volume method
Progress in Nuclear Energy, 2018Co-Authors: Alvaro Bernal, Jose E Roman, R Miro, G VerduAbstract:Abstract The spatial distribution of the Neutron flux within the core of nuclear reactors is a key factor in nuclear safety. The easiest and fastest way to determine it is by solving the eigenvalue problem of the Neutron Diffusion Equation, which only contains spatial derivatives. The approximation of these derivatives is performed by discretizing the geometry and using numerical methods. In this work, the authors used a finite volume method based on a polynomial expansion of the Neutron flux. Once these terms are discretized, a set of matrix Equations is obtained, which constitutes the eigenvalue problem. A very effective class of methods for the solution of eigenvalue problems are those based on projection onto a low-dimensional subspace, such as Krylov subspaces. Thus, the SLEPc library was used for solving the eigenvalue problem by means of the Krylov-Schur method, which also uses projection methods of PETSc for solving linear systems. This work includes a complete sensitivity analysis of different issues: mesh, polynomial terms, linear systems solvers and parallelization.
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assembly discontinuity factors for the Neutron Diffusion Equation discretized with the finite volume method application to bwr
Annals of Nuclear Energy, 2016Co-Authors: Alvaro Bernal, Jose E Roman, R Miro, G VerduAbstract:Abstract The Neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential Equation. In steady state conditions, the time derivative terms are zero and this Equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR. This eigenvalue problem has been solved by means of the SLEPc library.
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development of a finite volume inter cell polynomial expansion method for the Neutron Diffusion Equation
Journal of Nuclear Science and Technology, 2016Co-Authors: Alvaro Bernal, D Ginestar, Jose E Roman, R Miro, G VerduAbstract:Heterogeneous nuclear reactors require numerical methods to solve the Neutron Diffusion Equation (NDE) to obtain the Neutron flux distribution inside them, by discretizing the heterogeneous geometry in a set of homogeneous regions. This discretization requires additional Equations at the inner faces of two adjacent cells: Neutron flux and current continuity, which imply an excess of Equations. The finite volume method (FVM) is suitable to be applied to NDE, because it can be easily applied to any mesh and it is typically used in the transport Equations due to the conservation of the transported quantity within the volume. However, the gradient and face-averaged values in the FVM are typically calculated as a function of the cell-averaged values of adjacent cells. So, if the materials of the adjacent cells are different, the Neutron current condition could not be accomplished. Therefore, a polynomial expansion of the Neutron flux is developed in each cell for assuring the accomplishment of the flux and cur...
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resolution of the generalized eigenvalue problem in the Neutron Diffusion Equation discretized by the finite volume method
Abstract and Applied Analysis, 2014Co-Authors: Alvaro Bernal, D Ginestar, R Miro, G VerduAbstract:Numerical methods are usually required to solve the Neutron Diffusion Equation applied to nuclear reactors due to its heterogeneous nature. The most popular numerical techniques are the Finite Difference Method (FDM), the Coarse Mesh Finite Difference Method (CFMD), the Nodal Expansion Method (NEM), and the Nodal Collocation Method (NCM), used virtually in all Neutronic Diffusion codes, which give accurate results in structured meshes. However, the application of these methods in unstructured meshes to deal with complex geometries is not straightforward and it may cause problems of stability and convergence of the solution. By contrast, the Finite Element Method (FEM) and the Finite Volume Method (FVM) are easily applied to unstructured meshes. On the one hand, the FEM can be accurate for smoothly varying functions. On the other hand, the FVM is typically used in the transport Equations due to the conservation of the transported quantity within the volume. In this paper, the FVM algorithm implemented in the ARB Partial Differential Equations solver has been used to discretize the Neutron Diffusion Equation to obtain the matrices of the generalized eigenvalue problem, which has been solved by means of the SLEPc library.
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parallel resolution of the two group time dependent Neutron Diffusion Equation with public domain ode codes
IEEE International Conference on High Performance Computing Data and Analytics, 2004Co-Authors: Victor M Garcia, G Verdu, Vicente Vidal, J Garayoa, R MiroAbstract:In this paper it is shown how specialised codes for the resolution of ordinary differential Equations (FCVODE[3], DASPK[2]) can be used to solve efficiently the time dependent Neutron Diffusion Equation. Using these codes as basis, several new codes have been developed, combining the sequential and parallel versions of DASPK and FCVODE with different preconditioners. Their performance has been assessed using a two-dimensional benchmark (The TWIGL reactor).