Details
| Original language | English |
|---|---|
| Pages (from-to) | 46-55 |
| Number of pages | 10 |
| Journal | Advances in water resources |
| Volume | 49 |
| Early online date | 1 Aug 2012 |
| Publication status | Published - Dec 2012 |
Abstract
The automatic non-iterative second-order time-stepping scheme based on the temporal truncation error proposed by Kavetski et al. [Kavetski D, Binning P, Sloan SW. Non-iterative time-stepping schemes with adaptive truncation error control for the solution of Richards equation. Water Resour Res 2002;38(10):1211, http://dx.doi.org/10.1029/2001WR000720.] is implemented into the code of the HydroGeoSphere model. This time-stepping scheme is applied for the first time to the low-Rayleigh-number thermal Elder problem of free convection in porous media [van Reeuwijk M, Mathias SA, Simmons CT, Ward JD. Insights from a pseudospectral approach to the Elder problem. Water Resour Res 2009;45:W04416, http://dx.doi.org/10.1029/2008WR007421.], and to the solutal [Shikaze SG, Sudicky EA, Schwartz FW. Density-dependent solute transport in discretely-fractured geological media: is prediction possible? J Contam Hydrol 1998;34:273-91] problem of free convection in fractured-porous media. Numerical simulations demonstrate that the proposed scheme efficiently limits the temporal truncation error to a user-defined tolerance by controlling the time-step size. The non-iterative second-order time-stepping scheme can be applied to (i) thermal and solutal variable-density flow problems, (ii) linear and non-linear density functions, and (iii) problems including porous and fractured-porous media.
Keywords
- Density-driven flow, Numerical model, Time-stepping, Truncation error
ASJC Scopus subject areas
- Environmental Science(all)
- Water Science and Technology
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In: Advances in water resources, Vol. 49, 12.2012, p. 46-55.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-iterative adaptive time-stepping scheme with temporal truncation error control for simulating variable-density flow
AU - Hirthe, Eugenia M.
AU - Graf, Thomas
PY - 2012/12
Y1 - 2012/12
N2 - The automatic non-iterative second-order time-stepping scheme based on the temporal truncation error proposed by Kavetski et al. [Kavetski D, Binning P, Sloan SW. Non-iterative time-stepping schemes with adaptive truncation error control for the solution of Richards equation. Water Resour Res 2002;38(10):1211, http://dx.doi.org/10.1029/2001WR000720.] is implemented into the code of the HydroGeoSphere model. This time-stepping scheme is applied for the first time to the low-Rayleigh-number thermal Elder problem of free convection in porous media [van Reeuwijk M, Mathias SA, Simmons CT, Ward JD. Insights from a pseudospectral approach to the Elder problem. Water Resour Res 2009;45:W04416, http://dx.doi.org/10.1029/2008WR007421.], and to the solutal [Shikaze SG, Sudicky EA, Schwartz FW. Density-dependent solute transport in discretely-fractured geological media: is prediction possible? J Contam Hydrol 1998;34:273-91] problem of free convection in fractured-porous media. Numerical simulations demonstrate that the proposed scheme efficiently limits the temporal truncation error to a user-defined tolerance by controlling the time-step size. The non-iterative second-order time-stepping scheme can be applied to (i) thermal and solutal variable-density flow problems, (ii) linear and non-linear density functions, and (iii) problems including porous and fractured-porous media.
AB - The automatic non-iterative second-order time-stepping scheme based on the temporal truncation error proposed by Kavetski et al. [Kavetski D, Binning P, Sloan SW. Non-iterative time-stepping schemes with adaptive truncation error control for the solution of Richards equation. Water Resour Res 2002;38(10):1211, http://dx.doi.org/10.1029/2001WR000720.] is implemented into the code of the HydroGeoSphere model. This time-stepping scheme is applied for the first time to the low-Rayleigh-number thermal Elder problem of free convection in porous media [van Reeuwijk M, Mathias SA, Simmons CT, Ward JD. Insights from a pseudospectral approach to the Elder problem. Water Resour Res 2009;45:W04416, http://dx.doi.org/10.1029/2008WR007421.], and to the solutal [Shikaze SG, Sudicky EA, Schwartz FW. Density-dependent solute transport in discretely-fractured geological media: is prediction possible? J Contam Hydrol 1998;34:273-91] problem of free convection in fractured-porous media. Numerical simulations demonstrate that the proposed scheme efficiently limits the temporal truncation error to a user-defined tolerance by controlling the time-step size. The non-iterative second-order time-stepping scheme can be applied to (i) thermal and solutal variable-density flow problems, (ii) linear and non-linear density functions, and (iii) problems including porous and fractured-porous media.
KW - Density-driven flow
KW - Numerical model
KW - Time-stepping
KW - Truncation error
UR - http://www.scopus.com/inward/record.url?scp=84866669565&partnerID=8YFLogxK
U2 - 10.1016/j.advwatres.2012.07.021
DO - 10.1016/j.advwatres.2012.07.021
M3 - Article
AN - SCOPUS:84866669565
VL - 49
SP - 46
EP - 55
JO - Advances in water resources
JF - Advances in water resources
SN - 0309-1708
ER -