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In this paper, we propose a novel approach for coupling 2D/1D shallow waterflow models. Efficiently coupling these models is vital for simulating the flowand flooding of open channels. Currently, existing methods couple the modelseither at the channel lateral boundaries (lateral methods) or at the location,along the channel flow direction, where the two sub-domains intersect (frontalmethods). We classify these methods as horizontal methods since the couplingpoints are on the horizontal plane. The limitations of these methods includetheir inability to recover the 2D channel flow structure during floodingwithout losing efficiency, and their inability to switch between lateral andfrontal methods, based on the problem. Here, we propose a new paradigm which isto think of the channel flow as a two layer flow. This leads to the verticalcoupling method (VCM) which is able to recover 2D channel flow structurewithout losing efficiency, switch types depending on the flow and is a supersetof some existing methods. The VCM is based on a user chosen elevation abovewhich the user considers the channel to be full. From this elevation, all otherflow quantities are defined including the two layers. The flows in the lowerand upper layers are assumed to be 1D and 2D respectively, and the appropriateflow models with exchange terms are derived. The 2D shallow water flow model isretained for the floodplains. Finite volume methods (FVM) are formulated forthe flood model; the FVM with the operator splitting approach are alsoformulated to solve and couple the two layer channel flow models. We show thatthe resulting method (i) is well-balanced (ii) preserves the "no-numerical"flooding property (iii) preserves conservation properties and (iv) adapts tothe flow situation.

A two-layer approach for Coupling 1D/2D Shallow Water Flow Models