Section: New Results

Environmental and Astrophysical flows

Participants : Hervé Guillard, Boniface Nkonga, Marco Bilanceri, Maria-Vittoria Salvetti [University of Pisa, Italy] , Karim Elhakim [University Ains Shams, Egypt] .

The numerical approximation of a model coupling the shallow-water equations with a sediment transport equation for the morphodynamics has been studied. In shallow-water problems, time advancing can be carried out by explicit schemes. However, if the interaction with the mobile bed is weak, the characteristic time scales of the flow and of the sediment transport can be very different introducing time stiffness in the global problem. For this case, it is of great interest to use implicit schemes. The time integration stategy that we have devised is based on a defect-correction approach and on a time linearization, in which the flux Jacobians are computed through automatic differentiation. This work has been published in this reference (Linearized implicit time advancing and defect correction applied to sediment transport simulations Marco Bilanceri; François Beux; Imad Elmahi; Hervé Guillard; Maria Vittoria Salvetti Computers and Fluids, elsevier, 2012, 63, pp. 82-104). The aim of the present work is to investigate the behavior of this time scheme for different Riemann solvers, sediment transport models and situations related to environmental flows [12] . This activity takes place in the framework of the Euromediterranée 3+3 MedLagoon program and a PHC Imhotep program. A preliminary work has begun to apply this strategy to the study of the Burulus lake in Egypt.