Journal
ADVANCES IN WATER RESOURCES
Volume 25, Issue 8-12, Pages 899-944Publisher
ELSEVIER SCI LTD
DOI: 10.1016/S0309-1708(02)00063-5
Keywords
porous media; balance equations; phenomenological laws; constitutive relations; variable density; brine transport; saltwater intrusion; convection; thermohaline flow; fingering; Rayleigh number; instability; numerical simulation; finite element methods; adaptive methods; benchmarking
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We review the state of the art in modeling of variable-density flow and transport in porous media, including conceptual models for convection systems, governing balance equations, phenomenological laws, constitutive relations for fluid density and viscosity, and numerical methods for solving the resulting nonlinear multifield problems. The discussion of numerical methods addresses strategies for solving the coupled spatio-temporal convection process, consistent velocity approximation, and error-based mesh adaptation techniques. As numerical models for those nonlinear systems must be carefully verified in appropriate tests, we discuss weaknesses and inconsistencies of current model-verification methods as well as benchmark solutions. We give examples of field-related applications to illustrate specific challenges of further research, where heterogeneities and large scales are important. (C) 2002 Elsevier Science Ltd. All rights reserved.
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