TY - JOUR

T1 - Systematic investigation of non-Boussinesq effects in variable-density groundwater flow simulations

AU - Guevara Morel, Carlos R.

AU - Van Reeuwijk, Maarten

AU - Graf, Thomas

N1 - Publisher Copyright: © 2015 Elsevier B.V. All rights reserved.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - The validity of three mathematical models describing variable-density groundwater flow is systematically evaluated: (i) a model which invokes the Oberbeck-Boussinesq approximation (OB approximation), (ii) a model of intermediate complexity (NOB1) and (iii) a model which solves the full set of equations (NOB2). The NOB1 and NOB2 descriptions have been added to the HydroGeoSphere (HGS) model, which originally contained an implementation of the OB description. We define the Boussinesq parameter ερ = βω Δω where βω is the solutal expansivity and Δω is the characteristic difference in solute mass fraction. The Boussinesq parameter ερ is used to systematically investigate three flow scenarios covering a range of free and mixed convection problems: 1) the low Rayleigh number Elder problem (Van Reeuwijk et al., 2009), 2) a convective fingering problem (Xie et al., 2011) and 3) a mixed convective problem (Schincariol et al., 1994). Results indicate that small density differences (ερ ≤0.05) produce no apparent changes in the total solute mass in the system, plume penetration depth, center of mass and mass flux independent of the mathematical model used. Deviations between OB, NOB1 and NOB2 occur for large density differences (ε> 0.12), where lower description levels will underestimate the vertical plume position and overestimate mass flux. Based on the cases considered here, we suggest the following guidelines for saline convection: the OB approximation is valid for cases with ε;bsub; < 0.05, and the full NOB set of equations needs to be used for cases with ε > 0.10. Whether NOB effects are important in the intermediate region differ from case to case.

AB - The validity of three mathematical models describing variable-density groundwater flow is systematically evaluated: (i) a model which invokes the Oberbeck-Boussinesq approximation (OB approximation), (ii) a model of intermediate complexity (NOB1) and (iii) a model which solves the full set of equations (NOB2). The NOB1 and NOB2 descriptions have been added to the HydroGeoSphere (HGS) model, which originally contained an implementation of the OB description. We define the Boussinesq parameter ερ = βω Δω where βω is the solutal expansivity and Δω is the characteristic difference in solute mass fraction. The Boussinesq parameter ερ is used to systematically investigate three flow scenarios covering a range of free and mixed convection problems: 1) the low Rayleigh number Elder problem (Van Reeuwijk et al., 2009), 2) a convective fingering problem (Xie et al., 2011) and 3) a mixed convective problem (Schincariol et al., 1994). Results indicate that small density differences (ερ ≤0.05) produce no apparent changes in the total solute mass in the system, plume penetration depth, center of mass and mass flux independent of the mathematical model used. Deviations between OB, NOB1 and NOB2 occur for large density differences (ε> 0.12), where lower description levels will underestimate the vertical plume position and overestimate mass flux. Based on the cases considered here, we suggest the following guidelines for saline convection: the OB approximation is valid for cases with ε;bsub; < 0.05, and the full NOB set of equations needs to be used for cases with ε > 0.10. Whether NOB effects are important in the intermediate region differ from case to case.

KW - HydroGeoSphere

KW - Oberbeck-Boussinesq

KW - Variable-density flow

UR - http://www.scopus.com/inward/record.url?scp=84946145802&partnerID=8YFLogxK

U2 - 10.1016/j.jconhyd.2015.10.004

DO - 10.1016/j.jconhyd.2015.10.004

M3 - Article

C2 - 26540664

AN - SCOPUS:84946145802

VL - 183

SP - 82

EP - 98

JO - Journal of contaminant hydrology

JF - Journal of contaminant hydrology

SN - 0169-7722

ER -