Reaction-Convection-Diffusion Solver for CFD Applications on the Grid

This chapter presents a fast solver for reaction-convection-diffusion that performs efficiently on the grid. This solver uses the algorithm first introduced at the domain decomposition conference DD13 in 2001. A combination of techniques is used that consists of the method of characteristic for the convection term and the stabilization of the explicit treatment of the diffusion term with a posteriori filtering. The whole problem is then parametrized by space dependency. The stabilizing technique based on filtering is limited to grids that can be mapped to regular space discretization or grids that can be decomposed into subdomains with regular space discretization. The main mathematical idea is to construct a filtering technique that can remove the high frequencies to relax the constraint on the time step while keeping second order accuracy in space. The performance of the numerical solver is compared with other methods such as Krylov-Newton methods or operator splitting. The parallel performance of the solver is shown on a heterogeneous grid of parallel systems located in several universities. It is feasible to design efficient parallel algorithm for PDEs on metacomputing architecture with the help of a fruitful combination of domain decomposition and filtering.