A WELL BALANCED SCHEME FOR A MODEL OF ATM OSPHERE WITH GRAVITY

The numerical processing of problems arising in environment models of large scale atmospheric phenomenons involves the use of experimental d ata corresponding to the steady slate with a zero velocity. We need nu merical schemes which preserve this state; we call them well-balanced (W.B.) schemes. Since the gravity term corresponds here to a source te rm, the steady state corresponds to a balance between this term and th e fluxes. If this balance is not ensured, a numerical scheme can lead to some instability and nan physical behaviour. We propose the constru ction of a W.B., scheme for this model, by using the hydrostatic press ure as a potential, which transforms the source terms into fluxes, mak ing that way the numerical balance possible. This numerical stability is still preserved after a small perturbation of the steady state.