AbstractsEarth & Environmental Science

In this work we explore the properties of shallow water flows along channels with an obstacle on its bottom and a symmetric contraction, and provide a robust numerical algorithm to simulate such flows. Staring with the Saint-Venant equations for shallow water flows, a hyperbolic system of PDEs, we arrive at a non-linear algebraic system that equilibrium solutions must satisfy. We also determine the minimum data required to describe the flows and define the different possible regimes of the flow as determined by its Froude number, a dimensionless quantity. We pay special attention to discontinuous flows, where the fluid moving at high velocity upstream is forced to match slower flow conditions downstream by dissipating energy through a hydraulic jump. Several solutions illustrating the different types of flows are also presented so as to validate our algorithm and demonstrate its robustness. Advisors/Committee Members: Balbas, Jorge (advisor), Horn, Werner (committee member).