Numerical simulation of laminar flames at low Mach number by adaptive finite elements

We present an adaptive finite-element method for the simulation of reactive flows in general domains including reliable error control for quantities of physical interest. On the basis of computable a posteriori error bounds the mesh is locally adjusted by a hierarchical feedback process yielding economical mesh-size distributions for a prescribed maximum number of cells. The key feature is the computational evaluation of the sensitivity of the error with respect to the local residuals by solving an associated global dual problem. This general approach is applied for computing three examples of flames in two dimensions with an increasing degree of complexity, namely a simple diffusion flame described by the flame-sheet model, an ozone decomposition flame and a methane flame in a complex burner geometry using a detailed reaction mechanism.