Abstract
BACKGROUND: Instead of a 3d model, thehybrid model represents wave shoaling,breaking and runup by coupling Boussinesqtype and Saint-Venant models. It has gainedwide adoption: It simply switches-off/ondispersive terms but it has three problems:- Oscillations- Mesh convergence (lack of)- InstabilitiesIS THE HYBRID TRULY RELIABLE?IS THE HYBRID'S PDE WORTHSOLVING?METHODS1. Through Laplace transform, thetransmission conditions implicit in thehybrid model can be identified: Dirichlet +Neumann.2. An iterative method (Schwarz WaveformRelaxation, SWRM) is used to prove thewell-posedness by decomposing thedomain into two coupled models withtransmission conditions and iterating onthe traces of transmission conditions.3. If the initial condition is supported in oneside of the interface, then the couplingerror can be described as the differencebetween the hybrid and the one-waycoupling, controlled by a “reflectioncoefficient”RESULTS- The SWRM converges in 3 iterations, sothe problem is well-posed: YES.- The coupling error solves a Cauchyproblem with a filtered-reflected initialcondition- The SV to B case is always worse due tothe larger reflection coefficient and thegreater phase-speed