The optimized order 2 method. Application to convection-diffusion problems

In fluid dynamics, the convection-diffusion equation models for example the concentration of a pollutant in the air. We present an iterative, non-overlapping domain decem position method for solving this equation. The domain is divided into subdomains, and the physical problem is solved in each subdomain, with specific conditions at the interfaces, This permits to solve very big problems which couldn't be solved on only one processor. A reformulation of the problem leads to an equivalent problem where the unknowns are on the boundary of the subdomains [14]. The solving of this interface problem by a Krylov type algorithm [15] is done by the solving of independant problems in each subdomain, so it permits to use efficiently parallel computation. In order to have very fast convergence, we use differential interface conditions of order 1 in the normal direction and of order 2 in the tangential direction to the interface, which are optimized approximations of Absorbing Boundary Conditions (ABC) [13], [8]. We present simulations performed on the paragon intel at ONERA (100 processors), which show a very fast convergence, nearly independant both of the physical and the discretization parameters.