Upwelling and downwelling behavior in the Elder‐Voss‐Souza benchmark

Abstract

[1] The Elder-Voss-Souza (EVS) problem is a standard benchmark for the numerical simulation of variable-density flow and solute transport in a porous medium. However, a review of prior work shows that there is a wide variation in published results on plume structure that cannot entirely be explained by different choices of governing and constitutive equation or by discretization error and numerical error. This work presents results using a new numerical model and algorithms for a series of well-calibrated comparison tests that are designed to elucidate the issue. In addition to the factors mentioned above, we consider the effects of initial and boundary conditions, domain geometry, and problem parameters such as the length of the source boundary segment and the buoyancy parameter in the associated Rayleigh number. It is found that these are key parameters determining the upwelling/downwelling plume behavior. More specifically, the values chosen for the EVS problem lie close to critical values that separate odd and even plume numbers. Consequently, perturbations to the model, mesh, and simulation variables may lead to different plume behavior.

Insights from a pseudospectral approach to the Elder problem

“…Solution of equation (8) (26) on the transients and the steady state solutions of the Elder problem. We find that the transients are very sensitive to d [see also Woods and Carey, 2007]. As the transients ultimately determine the final steady state, d influences whether the system will end up in S 1 , S 2 or S 3 .…”

“…The problem is that since then, there have been a significant number of published Elder problem simulations which dramatically vary in the way the plumes develop and the number of plumes that remain once the system has reached steady state [Oldenburg and Pruess, 1995;Kolditz et al, 1997;Ackerer et al, 1999;Boufadel et al, 1999;Oltean and Bues, 2001;Frolkovic and de Schepper, 2000;Diersch and Kolditz, 2002]. These discrepancies have been attributed to various issues including mesh resolution, variation in numerical schemes and the use of different formulations for the governing equations [Diersch and Kolditz, 2002;Woods et al, 2003;Woods and Carey, 2007;Park and Aral, 2007;Al-Maktoumi et al, 2007]. More pertinently, using a bifurcation analysis based on a finite volume model, Johannsen [2003] demonstrated a consistent existence of three stable and a further eight unstable steady state solutions, significantly questioning the sensibility of using the Elder problem for benchmarking purposes.…”

Thermal plume transport from sand and gravel pits – Potential thermal impacts on cool water streams

“…Several investigators have found the computational results for the solutal transport version of this problem to be highly sensitive to the spatial and temporal discretization (e.g., Oldenburg and Pruess, 1995b;Holzbecher, 1998;Kolditz et al, 1998;Frolkovič and De Schepper, 2001;Diersch and Kolditz, 2002;Woods and Carey, 2007;AlMaktoumi et al, 2007), initial conditions (e.g., Frolkovič and De Schepper, 2001;Woods and Carey, 2007;van Reeuwijk et al, 2009), and the choice of the numerical algorithm used to approximate the transport equation, as well as the solver (e.g., Oldenburg and Pruess, 1995a;Holzbecher, 1998;Kolditz et al, 1998;Frolkovič and De Schepper, 2001;Diersch and Kolditz, 2002;Al-Maktoumi et al, 2007;Park and Aral, 2007). This has resulted in there being several solutions to the Elder problem presented in the literature.…”

“…Woods and Carey, 2007;Al-Maktoumi et al, 2007) as Ra increases above 60, the numerical solution becomes increasingly sensitive to the grid discretization and time step size.…”

Effects of salinity variations on pore water flow in salt marshes

“…Notwithstanding this uncertainty, there is also a question concerning the possibility of flow instability in the form of fingering flow induced by the upward density gradients at the platform. Rapid penetration of fingers would lead to more extensive and faster solute transport [Simmons et al, 2001;Stevens et al, 2009;Woods and Carey, 2007;Xie et al, 2011]. For a marsh system, the effect of unstable fingers may lead to enhanced exchange between the marsh sediment and tidal water.…”