Coupling 3-D Navier Stokes and 1-D Shallow Water

The present work addresses the problem of coupling hydrodynamical models with different spatial dimensions, which can be used in order to reduce the computational cost of river numerical models. We show that this problem can be tackled quite efficiently by designing a simple algorithm using techniques borrowed from domain decomposition theory. This algorithm is non intrusive, i.e. allows using existing numerical models with very few modifications. The method is illustrated on an academic test-case, namely a free surface flow in a bend-shaped channel. A 3-D Navier-Stokes model is coupled with a 1-D shallow water model, and results are compared to those obtained in a fully 3-D case. It is shown that the coupling algorithm provides an accurate solution, which can be improved thanks to an iterative algorithm (Schwarz method). This study is performed using the Mascaret-Telemac system.