We present an adaptive algorithm for low Mach number reacting flows with co
mplex chemistry. Our approach uses a form of the low Mach number equations
that discretely conserves both mass and energy. The discretization methodol
ogy is based on a robust projection formulation that accommodates large den
sity contrasts. The algorithm uses an operator-split treatment of stiff rea
ction terms and includes effects of differential diffusion. The basic compu
tational approach is embedded in an adaptive projection framework that uses
structured hierarchical grids with subcycling in time that preserves the d
iscrete conservation properties of the underlying single-grid algorithm. We
present numerical examples illustrating the performance of the method on b
oth premixed and non-premixed dames.