Non-reflecting boundary flux function for finite volume shallow-water models

An approach to implement non-reflecting boundary conditions in finite-volume based shallow-water models is presented. Shallow-water models are routinely applied to sections of rivers, estuaries, and coastal zones, introducing computational boundaries where no physical control is present, and necessitating a condition that supplies information to the model while it simultaneously allows disturbances from the interior to pass out unhampered. The approach presented here builds upon the finite-volume convention of constructing a Riemann problem at the interface between cells and then solving it with a flux function. Hence, non-reflecting boundary conditions are achieved using a non-reflecting flux function on cell faces aligned with open boundaries. Numerical tests show that the non-reflecting flux function performs extremely well when waves advance toward the boundary with a small incident angle (approximately less than 45° from the boundary normal direction), while very minor reflections are present when the incident angle is larger. The presence of minor reflections, when the incident angle is large, is consistent with non-reflecting conditions previously implemented in finite-difference based schemes.