Operator Splitting and Adaptive Mesh Refinement

Numerical Combustion with detailed chemical kinetics is a very challenging problem. The set of the species conservation equations is mathematically very stiff. The stability of the explicit projection schemes for such problems requires a very strict CFL condition, limiting the maximum timestep to a few nanoseconds. To overcome this limitation, semi-implicit stiff integration is carried out in an operator-split projection scheme. A set of ODEs is solved implicitly using commercially available stiff ODE solvers during the process. The next limiting CFL condition, that does not allow the full potential usage of semi-implicit scheme, is the diffusion of intermediate species like H ion. Diffusion sub-stepping with Operator-Splitting is performed to get around this problem. As a result, stable time stepping increases from few nanoseconds to hundreds of nanoseconds.

These schemes are currently being used to investigate the impact of thermal interactions between the heat-conducting burner plates (flame-holders) and premixed flames. Their role in static and dynamic stability is being investigated. These are direct simulations with all the time and length scales resolved. Adaptive Mesh Refinement procedures are being incorporated in the codes to be able to increase the size of the simulation domain.