An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion

We investigate adaptive finite element methods for low Mach, steady, laminar combustion. The finite element discretization of the flame equations involves least squares control of streamline derivatives and pressure-velocity coupling as well as a new shock capturing term based on nonlinear crosswind diffusion yielding a suitable discrete maximum principle for the discrete solution. A posteriori error estimates derived from the dual weighted residual method are used to refine the mesh adaptively. Numerical results are presented for a Bunsen flame with simple chemistry on locally refined as well as fully unstructured Delaunay meshes. Solution quality is evaluated in terms of overall flame characteristics - including length, lift off and width - as well as undershoots in species and temperature profiles.