Convergence of a stationary profiles scheme for the first order quasilinear equations with source terms

When a source term is present, the constants are no longer solutions to quasilinear equations. Some numerical techniques based on this property need to be generalized. A stationary profile scheme uses an approximate solution made of stationary solutions in each cell. We propose such a scheme, for which we prove some results of stability and convergence towards the entropy solution. The numerical tests show that this scheme is well adapted to the simulation of well balanced states, and often far better than the usual splitting methods. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.