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WATER RESOURCES RESEARCH, VOL. 41, W01019, doi:10.1029/2003WR002777, 2005

Numerical simulation of double-diffusive finger convection

Joseph D. Hughes

Department of Geology, University of South Florida, Tampa, Florida, USA


Ward E. Sanford

U.S. Geological Survey, Reston, Virginia, USA


H. Leonard Vacher

Department of Geology, University of South Florida, Tampa, Florida, USA


Abstract

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double-diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density-dependent, saturated-unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute-transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute-transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High-resolution data from a double-diffusive Hele-Shaw experiment, initially in a density-stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double-diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

Received 17 October 2003; accepted 7 October 2004; published 29 January 2005.

Keywords: double diffusive convection; variable-density flow and transport.

Index Terms: 1832 Hydrology: Groundwater transport; 1831 Hydrology: Groundwater quality; 1884 Hydrology: Water supply; 1899 Hydrology: General or miscellaneous.

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Citation: Hughes, J. D., W. E. Sanford, and H. L. Vacher (2005), Numerical simulation of double-diffusive finger convection, Water Resour. Res., 41, W01019, doi:10.1029/2003WR002777.