Two-Layer Shallow Water System: A Relaxation Approach

The two-layer shallow water system is an averaged flow model. It forms a nonconservative system which is only conditionally hyperbolic. The coupling between the layers, due to the hydrostatic pressure assumption, does not provide explicit access to the system eigenstructure, which is inconvenient for Riemann solution based numerical schemes. We consider a relaxation approach which offers greater decoupling and accessible eigenstructure. The stability of the model is discussed. Numerical results are shown for unsteady flows as well as for smooth and nonsmooth steady flows.