Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix
This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin fini...
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| Autor*in: |
Watanabe, Norihiro [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. |
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| Übergeordnetes Werk: |
Enthalten in: Water resources research - Hoboken, NJ : Wiley, 1965, 51(2015), 7, Seite 5855-5868 |
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| Übergeordnetes Werk: |
volume:51 ; year:2015 ; number:7 ; pages:5855-5868 |
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| DOI / URN: |
10.1002/2015WR017164 |
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| 520 | |a This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix | ||
| 540 | |a Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. | ||
| 650 | 4 | |a solute transport | |
| 650 | 4 | |a discrete fracture | |
| 650 | 4 | |a numerical stability | |
| 650 | 4 | |a Finite element analysis | |
| 650 | 4 | |a Nonlinear programming | |
| 700 | 1 | |a Kolditz, Olaf |4 oth | |
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10.1002/2015WR017164 doi PQ20160617 (DE-627)OLC1965569412 (DE-599)GBVOLC1965569412 (PRQ)p1840-c16597bdb405afd878db587c6a5465f452ba2639aaf61e1d29b7572219cda5ae0 (KEY)0046260820150000051000705855numericalstabilityanalysisoftwodimensionalsolutetr DE-627 ger DE-627 rakwb eng 550 DNB 38.85 bkl Watanabe, Norihiro verfasserin aut Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming Kolditz, Olaf oth Enthalten in Water resources research Hoboken, NJ : Wiley, 1965 51(2015), 7, Seite 5855-5868 (DE-627)129088285 (DE-600)5564-5 (DE-576)014422980 0043-1397 nnns volume:51 year:2015 number:7 pages:5855-5868 http://dx.doi.org/10.1002/2015WR017164 Volltext http://onlinelibrary.wiley.com/doi/10.1002/2015WR017164/abstract http://search.proquest.com/docview/1704792786 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO GBV_ILN_2027 GBV_ILN_4219 38.85 AVZ AR 51 2015 7 5855-5868 |
| spelling |
10.1002/2015WR017164 doi PQ20160617 (DE-627)OLC1965569412 (DE-599)GBVOLC1965569412 (PRQ)p1840-c16597bdb405afd878db587c6a5465f452ba2639aaf61e1d29b7572219cda5ae0 (KEY)0046260820150000051000705855numericalstabilityanalysisoftwodimensionalsolutetr DE-627 ger DE-627 rakwb eng 550 DNB 38.85 bkl Watanabe, Norihiro verfasserin aut Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming Kolditz, Olaf oth Enthalten in Water resources research Hoboken, NJ : Wiley, 1965 51(2015), 7, Seite 5855-5868 (DE-627)129088285 (DE-600)5564-5 (DE-576)014422980 0043-1397 nnns volume:51 year:2015 number:7 pages:5855-5868 http://dx.doi.org/10.1002/2015WR017164 Volltext http://onlinelibrary.wiley.com/doi/10.1002/2015WR017164/abstract http://search.proquest.com/docview/1704792786 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO GBV_ILN_2027 GBV_ILN_4219 38.85 AVZ AR 51 2015 7 5855-5868 |
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10.1002/2015WR017164 doi PQ20160617 (DE-627)OLC1965569412 (DE-599)GBVOLC1965569412 (PRQ)p1840-c16597bdb405afd878db587c6a5465f452ba2639aaf61e1d29b7572219cda5ae0 (KEY)0046260820150000051000705855numericalstabilityanalysisoftwodimensionalsolutetr DE-627 ger DE-627 rakwb eng 550 DNB 38.85 bkl Watanabe, Norihiro verfasserin aut Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming Kolditz, Olaf oth Enthalten in Water resources research Hoboken, NJ : Wiley, 1965 51(2015), 7, Seite 5855-5868 (DE-627)129088285 (DE-600)5564-5 (DE-576)014422980 0043-1397 nnns volume:51 year:2015 number:7 pages:5855-5868 http://dx.doi.org/10.1002/2015WR017164 Volltext http://onlinelibrary.wiley.com/doi/10.1002/2015WR017164/abstract http://search.proquest.com/docview/1704792786 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO GBV_ILN_2027 GBV_ILN_4219 38.85 AVZ AR 51 2015 7 5855-5868 |
| allfieldsGer |
10.1002/2015WR017164 doi PQ20160617 (DE-627)OLC1965569412 (DE-599)GBVOLC1965569412 (PRQ)p1840-c16597bdb405afd878db587c6a5465f452ba2639aaf61e1d29b7572219cda5ae0 (KEY)0046260820150000051000705855numericalstabilityanalysisoftwodimensionalsolutetr DE-627 ger DE-627 rakwb eng 550 DNB 38.85 bkl Watanabe, Norihiro verfasserin aut Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming Kolditz, Olaf oth Enthalten in Water resources research Hoboken, NJ : Wiley, 1965 51(2015), 7, Seite 5855-5868 (DE-627)129088285 (DE-600)5564-5 (DE-576)014422980 0043-1397 nnns volume:51 year:2015 number:7 pages:5855-5868 http://dx.doi.org/10.1002/2015WR017164 Volltext http://onlinelibrary.wiley.com/doi/10.1002/2015WR017164/abstract http://search.proquest.com/docview/1704792786 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO GBV_ILN_2027 GBV_ILN_4219 38.85 AVZ AR 51 2015 7 5855-5868 |
| allfieldsSound |
10.1002/2015WR017164 doi PQ20160617 (DE-627)OLC1965569412 (DE-599)GBVOLC1965569412 (PRQ)p1840-c16597bdb405afd878db587c6a5465f452ba2639aaf61e1d29b7572219cda5ae0 (KEY)0046260820150000051000705855numericalstabilityanalysisoftwodimensionalsolutetr DE-627 ger DE-627 rakwb eng 550 DNB 38.85 bkl Watanabe, Norihiro verfasserin aut Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix Nutzungsrecht: © 2015. American Geophysical Union. All Rights Reserved. solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming Kolditz, Olaf oth Enthalten in Water resources research Hoboken, NJ : Wiley, 1965 51(2015), 7, Seite 5855-5868 (DE-627)129088285 (DE-600)5564-5 (DE-576)014422980 0043-1397 nnns volume:51 year:2015 number:7 pages:5855-5868 http://dx.doi.org/10.1002/2015WR017164 Volltext http://onlinelibrary.wiley.com/doi/10.1002/2015WR017164/abstract http://search.proquest.com/docview/1704792786 GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-GEO SSG-OLC-FOR SSG-OPC-GGO GBV_ILN_2027 GBV_ILN_4219 38.85 AVZ AR 51 2015 7 5855-5868 |
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We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. 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Watanabe, Norihiro |
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Watanabe, Norihiro ddc 550 bkl 38.85 misc solute transport misc discrete fracture misc numerical stability misc Finite element analysis misc Nonlinear programming Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix |
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550 DNB 38.85 bkl Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix solute transport discrete fracture numerical stability Finite element analysis Nonlinear programming |
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Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix |
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numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix |
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Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix |
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This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix |
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This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix |
| abstract_unstemmed |
This work reports numerical stability conditions in two‐dimensional solute transport simulations including discrete fractures surrounded by an impermeable rock matrix. We use an advective‐dispersive problem described in Tang et al. (1981) and examine the stability of the Crank‐Nicolson Galerkin finite element method (CN‐GFEM). The stability conditions are analyzed in terms of the spatial discretization length perpendicular to the fracture, the flow velocity, the diffusion coefficient, the matrix porosity, the fracture aperture, and the fracture longitudinal dispersivity. In addition, we verify applicability of the recently developed finite element method‐flux corrected transport (FEM‐FCT) method by Kuzmin ( ) to suppress oscillations in the hybrid system, with a comparison to the commonly utilized Streamline Upwinding/Petrov‐Galerkin (SUPG) method. Major findings of this study are (1) the mesh von Neumann number (Fo) ≥ 0.373 must be satisfied to avoid undershooting in the matrix, (2) in addition to an upper bound, the Courant number also has a lower bound in the fracture in cases of low dispersivity, and (3) the FEM‐FCT method can effectively suppress the oscillations in both the fracture and the matrix. The results imply that, in cases of low dispersivity, prerefinement of a numerical mesh is not sufficient to avoid the instability in the hybrid system if a problem involves evolutionary flow fields and dynamic material parameters. Applying the FEM‐FCT method to such problems is recommended if negative concentrations cannot be tolerated and computing time is not a strong issue. The von Neumann number ≥ 0.373 is required to avoid undershooting in the matrix The Courant number has a lower bound in the fracture for low dispersivity The FEM‐FCT method can suppress oscillations in both the fracture and the matrix |
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Numerical stability analysis of two‐dimensional solute transport along a discrete fracture in a porous rock matrix |
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