The Experts below are selected from a list of 4719 Experts worldwide ranked by ideXlab platform
Gema Verdú - One of the best experts on this subject based on the ideXlab platform.
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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, Jose E Roman, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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.
Alvaro Bernal - One of the best experts on this subject based on the ideXlab platform.
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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, Jose E Roman, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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.
Rafael Miró - One of the best experts on this subject based on the ideXlab platform.
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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, Jose E Roman, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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.
Damián Ginestar - One of the best experts on this subject based on the ideXlab platform.
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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, Jose E Roman, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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, Rafael Miró, Damián Ginestar, Gema VerdúAbstract: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.
Jacques Sainte-marie - One of the best experts on this subject based on the ideXlab platform.
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Approximation of the hydrostatic Navier-Stokes system for density stratified flows by a multilayer model. Kinetic interpretation and numerical solution.
Journal of Computational Physics, 2011Co-Authors: Emmanuel Audusse, Marie-odile Bristeau, Marica Pelanti, Jacques Sainte-marieAbstract:We present a multilayer Saint-Venant system for the numerical simulation of free surface density-stratified flows over variable topography. The proposed model formally approxi- mates the hydrostatic Navier-Stokes equations with a density that varies depending on the spatial and temporal distribution of a Transported Quantity such as temperature or salinity. The derivation of the multilayer model is obtained by a Galerkin-type vertical dis- cretization of the Navier-Stokes system with piecewise constant basis functions. In con- trast with classical multilayer models in the literature that assume immiscible fluids, we allow here for mass exchange between layers. We show that the multilayer system admits a kinetic interpretation, and we use this result to formulate a robust finite volume scheme for its numerical approximation. Several numerical experiments are presented, including simulations of wind-driven stratified flows.
