Comparison of different 2nd order formulations for the solution of the 2D groundwater flow problem over irregular triangular meshes

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Abstract

Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution of the 2D linear groundwater flow problem over domain discretized by means of triangular irregular meshes. The numerical results of the modified MHFE procedure are compared with the results of a modified 2 nd spatial approximation order Finite Volume (FV2) formulation [2], as well as with the results given by the standard MHFE method. The FV2 approach is equivalent to the standard MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. The modified MHFE formulation is equivalent to the standard MHFE approach in both isotropic and heterogeneous medium cases, using regular or irregular computational meshes, but has a smaller number of unknowns for given mesh geometry
Lingua originaleEnglish
pagine (da-a)45-57
Numero di pagine13
RivistaWSEAS Transactions on Fluid Mechanics
Volume2009
Stato di pubblicazionePublished - 2009

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Groundwater Flow
Groundwater flow
Triangular Mesh
ground water
Irregular
mesh
Mesh
Finite Element
formulations
Formulation
isotropic media
Finite element method
Hybrid Method
Petroleum reservoirs
Finite Volume
Potential flow
Advection
finite element method
Finite Element Method
Conservation

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Fluid Flow and Transfer Processes
  • Physics and Astronomy(all)
  • Ocean Engineering
  • Modelling and Simulation

Cita questo

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title = "Comparison of different 2nd order formulations for the solution of the 2D groundwater flow problem over irregular triangular meshes",
abstract = "Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution of the 2D linear groundwater flow problem over domain discretized by means of triangular irregular meshes. The numerical results of the modified MHFE procedure are compared with the results of a modified 2 nd spatial approximation order Finite Volume (FV2) formulation [2], as well as with the results given by the standard MHFE method. The FV2 approach is equivalent to the standard MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. The modified MHFE formulation is equivalent to the standard MHFE approach in both isotropic and heterogeneous medium cases, using regular or irregular computational meshes, but has a smaller number of unknowns for given mesh geometry",
author = "Tullio Tucciarelli and Costanza Arico'",
year = "2009",
language = "English",
volume = "2009",
pages = "45--57",
journal = "WSEAS Transactions on Fluid Mechanics",
issn = "1790-5087",
publisher = "World Scientific and Engineering Academy and Society",

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TY - JOUR

T1 - Comparison of different 2nd order formulations for the solution of the 2D groundwater flow problem over irregular triangular meshes

AU - Tucciarelli, Tullio

AU - Arico', Costanza

PY - 2009

Y1 - 2009

N2 - Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution of the 2D linear groundwater flow problem over domain discretized by means of triangular irregular meshes. The numerical results of the modified MHFE procedure are compared with the results of a modified 2 nd spatial approximation order Finite Volume (FV2) formulation [2], as well as with the results given by the standard MHFE method. The FV2 approach is equivalent to the standard MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. The modified MHFE formulation is equivalent to the standard MHFE approach in both isotropic and heterogeneous medium cases, using regular or irregular computational meshes, but has a smaller number of unknowns for given mesh geometry

AB - Mixed and Mixed Hybrid Finite Elements (MHFE) methods have been widely used in the last decade for simulation of groundwater flow problem, petroleum reservoir problems, potential flow problems, etc. The main advantage of these methods is that, unlike the classical Galerkin approach, they guarantee local and global mass balance, as well the flux continuity between inter-element sides. The simple shape of the control volume, where the mass conservation is satisfied, makes also easier to couple this technique with a Finite Volume technique in the time splitting approach for the solution of advection-dispersion problems. In the present paper, a new MHFE formulation is proposed for the solution of the 2D linear groundwater flow problem over domain discretized by means of triangular irregular meshes. The numerical results of the modified MHFE procedure are compared with the results of a modified 2 nd spatial approximation order Finite Volume (FV2) formulation [2], as well as with the results given by the standard MHFE method. The FV2 approach is equivalent to the standard MHFE approach in the case of isotropic medium and regular or mildly irregular mesh, but has a smaller number of unknowns and better matrix properties. In the case of irregular mesh, an approximation is proposed to maintain the superior matrix properties of the FV2 approach, with the consequent introduction of a small error in the computed solution. The modified MHFE formulation is equivalent to the standard MHFE approach in both isotropic and heterogeneous medium cases, using regular or irregular computational meshes, but has a smaller number of unknowns for given mesh geometry

UR - http://hdl.handle.net/10447/38752

UR - http://www.worldses.org/journals/fluid/fluid-2009.htm

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VL - 2009

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EP - 57

JO - WSEAS Transactions on Fluid Mechanics

JF - WSEAS Transactions on Fluid Mechanics

SN - 1790-5087

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