Porous Shallow-Water Equations Model with Disambiguation of Multiple Solutions

Abstract

Porous shallow-water equations (PSWE) are a mathematical model for urban flooding simulation that has gained popularity because of its modest computational burden. Under certain initial conditions, PSWE may admit multiple exact solutions. This implies that (i) a criterion is required to identify the unique physically relevant solution among the alternatives, and that (ii) the corresponding numerical models should incorporate this criterion. In the present paper, a procedure for the disambiguation of PSWE multiple exact solutions is proposed and a 1-d PSWE numerical scheme from the literature is modified to embed the disambiguation ability.

Keywords

• shallow-water equations
• porosity
• urban flooding
• non-conservative products