Maximal dissipation and shallow water flow -- the dam-break problem

TL;DR

This paper investigates the shallow water flow over a dam with a bed jump, using the maximal dissipation principle to determine the flow's behavior and solution uniqueness.

Contribution

It introduces a novel approach applying the maximal dissipation principle to shallow water flow with a bed jump, ensuring bounded solutions and establishing wave connections.

Findings

Solutions stay bounded with shadow wave approximation.

Maximal dissipation principle ensures unique wave connections.

Flow behavior over the dam is characterized by these methods.

Abstract

The shallow water system with a bed jump describes a fluid flow over a dam, represented by a simple step function with the Riemann initial data is such that the vacuum is on the right-hand side. The main question is whether the fluid will stay on the left-hand side of the dam. After approximating the step function space derivative with a fixed shadow wave, solutions to that problem stay bounded. A proper connection between waves on both sides of the dam, and a unique solution afterward is found by using the maximal dissipation principle.