Boundary Value Problems for the Inviscid Primitive Equations in Limited Domain

Antoine Rousseau (1) , Roger M. Temam (2) , Joe Tribbia (3)

1 MOISE - Modelling, Observations, Identification for Environmental Sciences
2 ISC - Institute for Scientific Computing and Applied Mathematics
3 CGD - Climate and Global Dynamics Division [Boulder]

This work aims to contribute to what is considered as a major computational issue for the geophysical fuid dynamics (GFD) for the coming years, that is the boundary conditions for numerical computations in a limited domain, with a boundary that has (at least partly) no physical justification. Numerical computations in limited domains in ocean and atmosphere are "constantly" required (and sometimes lead to commercial softwares) in order to provide forecasts for agriculture, tourism industry, insurances, aircraft navigation, etc. This article focuses on the nonviscous primitive equations in a limited domain, in space dimension 2, 2.5 and 3 and provides in each case a set of boundary conditions wich is shown to lead to a well-posed problem. The suitability of these new boundary conditions is also computationnally evidenced in space dimension two.

Mots clés: Inviscid Primitive Equations; Open Boundary Conditions; Well-posedness; Numerical Simulations

Domaines: Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]; Equations aux dérivées partielles [math.AP]

Antoine Rousseau, Roger M. Temam, Joe Tribbia. Boundary Value Problems for the Inviscid Primitive Equations in Limited Domain. Roger Temam and Joe Tribbia. Computational Methods for the Atmosphere and the Oceans, 14, Elsevier, pp.481-576, 2009, Handbook on Numerical Analysis, ⟨10.1016/S1570-8659(08)00211-1⟩. ⟨inria-00324224⟩