An energetically consistent viscous sedimentation model

Jean de Dieu Zabsonré (1) , Carine Lucas (2) , Enrique D. Fernandez-Nieto (3)

1 UJZK - Université Joseph Ki-Zerbo [Université de Ouagadougou, Burkina Faso]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
3 IMUS - Departamento de Matemática Aplicada I

In this paper we consider a two dimensional viscous sedimentation model which is a viscous Shallow-Water system coupled with a diffusive equation that describes the evolution of the bottom. For this model, we prove the stability of weak solutions for periodic domains and give some numerical experiments. We also discuss around various discharge quantity choices.

Mots clés: Sedimentation; shallow water; viscous models; energetic consistency; stability

Domaines: Equations aux dérivées partielles [math.AP]

Jean de Dieu Zabsonré, Carine Lucas, Enrique D. Fernandez-Nieto. An energetically consistent viscous sedimentation model. Mathematical Models and Methods in Applied Sciences, 2009, 19 (3), pp.477-499. ⟨hal-00445677⟩