Two linearized problems of shallow water flows

Christian Licht (1) , Tran Thu Ha (2) , Quoc Phong Vu (3)

1 M3 - Modélisation Mathématique en Mécanique
2 Institute of Mechanics
3 Department of Mathematics

A mathematical analysis, based on the theory of semi-groups of operators on Hilbert space, of linearized problems involving Saint-Venant equations governing shallow water flows is carried out. The first problem concerns the classical linearized Saint-Venant problem, while the second deals with a water quality problem: the evolution of a concentration of products in a flow solution of the first problem. The method seems capable to take into account thermal and multi-phase effects.

Mots clés: Shallow water flows; Linearized Saint-Venant equations; Semi-group of operators

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Christian Licht, Tran Thu Ha, Quoc Phong Vu. Two linearized problems of shallow water flows. Thermal Hydrodynamics of Multiphase Flows and Applications, May 2009, Vietnam. pp.117-120. ⟨hal-00744110⟩