Timescale interpolation and no-neighbour discretization for a 1D finite-volume Saint-Venant solver

A new finite-volume numerical method for the one-dimensional (1D) Saint-Venant equations for unsteady open-channel flow is developed and tested. The model uses a recently-developed conservative finite-volume formulation that is inherently well-balanced for natural channels. A new timescale interpolation approach provides transition between 1st-order upwind and 2nd-order central interpolation schemes for supercritical and subcritical flow, respectively. This interpolation meets a proposed "no-neighbour" criterion for simplicity in future parallel implementation. Tests with a highly-resolved transitional flow and a coarsely-resolved natural channel show that the method is stable and accurate when applied with a flowrate damping algorithm that limits propagation of energy down to subgrid scales.