Physics Based Wave Generation for the Shallow Water Equations

Abstract: In this report we study systems governed by the Saint-Venant shallow water equations interacting with boundary conditions including control. We derive closed form formulas for the open-loop behavior. These formulas rely on first, second and third order approximations which are based on a perturbation that we develop. Properties of these solutions are studied and comparisons with existing non-linear solver solutions are carried out. The main advantage of our methodology is to provide computation efficient formulas that can be implemented for real-time calculations.