A multi-level local defect correction technique for laminar flame simulation

We present a numerical algorithm to solve the low-Mach number approximation of the conservation laws for laminar flames. Elements of our 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. Boundary value problems for laminar flames are characterised by a high activity region, the so-called flame front, where the solution varies very rapidly, whereas outside this region the solution is very smooth. 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 flame on a slit burner.