A pressure correction local defect correction algorithm for laminar flame simulation

We present a numerical algorithm to solve the zero-Mach number approximation of the governing equations for laminar flames. The ingredients of the algorithm are a Pressure Correction (PC) method to decouple the computation of velocity and pressure, and a multi-level Local Defect Correction (LDC) method to solve the resulting set of (non)linear boundary value problems. The PC method is based on a constraint equation, rather than the continuity equation, describing expansion of the gas mixture due to combustion. Moreover, we combine the PC method with implit Euler time integration to compute steady flames. Boundary value problems for laminar flames are characterised by a high activity region, the so-called flame front, where the solution varies rapidly. The basic idea of the LDC method is to compute a global coarse grid solution, that is accurate enough to represent the solution outside the flame front, and a sequence of local fine grid solutions to capture all the details in the flame front. Moreover, these fine grid solutions are subsequently used to improve the coarse grid solution by a defect correction technique. We have applied our PC LDC algorithm to simulate a two-dimensional methane/air flame