Variable density flow and solute transport simulation of regional aquifers containing a narrow freshwater‐saltwater transition zone

Abstract

Variable density flow and solute transport simulation of aquifer systems containing narrow transition zones between freshwater and saltwater requires particular attention to certain aspects of the numerical method and its application to be successful. Typically, only cases involving wide transition zones have been simulated with variable density transport models, possibly because of inaccuracies in the modeling approaches used. The major components of a successful approach are threefold. First, functionally consistent approximation of terms involved in fluid velocity calculations is necessary. In the case of Galerkin finite element methodology, a significant modification is required to the standard approach in order to achieve consistency. Second, the simulator must be verified in a particular series of tests. The usual tests using Henry's problem for verification of density-dependent transport simulators are inadequate to check for consistency of the velocity approximations and for the accuracy of simulating flow driven by bouyancy forces. Third, adequately fine spatial discretization is required when applying the simulator for spatial stability of the numerical transport solution and to allow accurate representation of narrow transition zones and the effects of low transverse dispersivity. The effectiveness of this approach is demonstrated through simulation of the flow of fresh and saline groundwater in the layered basalt aquifer of southern Oahu, Hawaii. The transition zone in this regional flow system is narrow except near the discharge area where it is broadly dispersed. Simulation of this common situation with an inconsistent approximation gives grossly incorrect results, while simulation with a consistent model provides a robust tool for analysis of system hydrology. 1851

Numerical error in groundwater flow and solute transport simulation

“…While it is welldefined and difficult to simulate, it does not have wellunderstood and consistent results. It is undeniably a much more stringent test than the comparable Henry problem [ Henry, 1964;Croucher and O'Sullivan, 1995;Benson et al, 1998;Voss and Souza, 1987] and so remains valuable, but if we expect a benchmark to distinguish between good and better methods of simulation, then the Elder problem is of limited usefulness. Codes capable of simulating the Elder problem do not necessarily agree on the results of other problems Woods et al, 1999], so it is clear that there is a need for even more rigorous test problems.…”

“…This implies that SUTRA is numerically unstable whenever the hydrodynamic dispersivity is zero. However, the code has been used successfully for simulations without hydrodynamic dispersivity, such as the Henry and Elder problems [Voss, 1984;Voss and Souza, 1987].…”

“…[40] The test problem in this case is Elder's ''shortheater'' problem, a heat flow problem [Elder, 1967] which was converted for use with solute-transport codes by Voss and Souza [1987]. It is one of the standard benchmark problems for variable-density flow and transport.…”

“…[49] Thus for a month-long time step (2.628 Â 10 6 s), as used by Voss and Souza [1987], the maximum numerical dispersion coefficients will be D xy N = ±2.37 Â 10 À5 m 2 s À1 and D xx N = D yy N = 1.18 Â 10 À5 m 2 s À1 which are an order of magnitude larger than the molecular diffusion coefficient, as D = 3.565 Â 10 À6 m 2 s À1 . At more typical velocities, D xy N = ±6.570 Â 10 À7 m 2 s À1 and D xx N = D yy N = 3.285 Â 10 À7 m 2 s À1 , which is smaller than the diffusion coefficient.…”

“…A modified SUTRA code, in which the numerical dispersion is calculated and subtracted, produces better results. The much more challenging Elder problem [Elder, 1967;Voss and Souza, 1987] is then considered. Calculation of its numerical dispersion coefficients and numerical stability show that the Elder problem is prone to error.…”