Steady-state density-driven flow and transport: Pseudo-transient parameter continuation

•Pseudo-transient parameter solves steady-state density-dependent problems.•The method is demonstrated to be robust and efficient in solving nonlinear steady states.•The method is straightforward to be implemented into the existing numerical models. Density-driven flow and transport is one of the dominant physical processes in coastal aquifer systems. To better manage water resources in coastal areas, the interactions need to be understood between freshwater and denser seawater. Numerical models often suffer from excessive computational cost to simulate the equilibrium steady state due to the nonlinear nature of the governing equations to describe density-driven flow. This study suggests a pseudo-transient parameter continuation (PTPC) approach which combines two general solution strategies for nonlinear steady-state equations: the pseudo-transient continuation (PTC) and parameter continuation (PC) methods. The new method gradually adjusts the maximum density (or parameter continuation) in the transient simulation framework (or pseudo-transient). The PTPC method is generally supposed to converge as in PTC and as efficiently as PC when the scheduling for parameter adjustment is set to be optimal. Through a proof-of-concept example, it is illustrated that the solution path to the steady state in PTPC is in between the paths from the PTC and PC approaches, depending on the level of aggressiveness of the parameter adjustment scheduling. As yet being empirical, the PTPC approach is promising and can be applicable to efficiently solve other steady-state nonlinear equations. The method was successfully applied to characterize and better understand the groundwater flow system in the Suruga Bay area, Japan.