  We present an algorithm for the numerical solution of the equations governing
combustion in porous inert media. The discretization of the flow problem is
performed by the mixed finite element method, the transport problems are
discretized by a cell-centered finite volume method. The resulting nonlinear
equations are lineararized with Newton's method, the linearized systems are
solved with a multigrid algorithm. Both subsystems are recoupled again in a
Picard iteration. Numerical simulations based on a simplified model show how
regions with different porosity stabilize the reaction zone inside the porous
burner.
