Space–Time Domain Decomposition with Finite Volumes for Porous Media Applications

We present an extension of the Optimized Schwarz Waveform Relaxation method with Robin transmission conditions to finite volume schemes of DDFV type (Discrete Duality Finite Volumes) for solving heterogeneous time-dependent advection-diffusion problems. We propose a new strategy which is well adapted to domain decomposition for coupling upwind discretization of the convection with diffusion in the context of a finite volume method. The method is proven to be well posed and we prove the convergence of the iterative algorithm. Then we present numerical results to illustrate the method.