Oberseminar Mathematical Fluid Dynamics

Shallow water models are derived under some smallness assumptions with the simplest model being sometimes called Saint-Venant system. By retaining more terms, we get higher order versions with the shear shallow water model being one such model, where some shear effects are present. This leads to a non-conservative system whose approximation poses some challenges. I will explain our efforts so far in the direction of path conservative methods, and point out many open questions