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Numerical simulation of reacting flows with comprehensive kinetics is one of the most demanding areas of computational fluid dynamics. High-fidelity modeling requires accurate fluid mechanics, detailed models for multicomponent transport and detailed chemical mechanisms. Spatial and temporal requirements based on integration of the compressible reacting Navier Stokes equations on a uniform mesh lead to prohibitive estimates for the computational cost. In this talk we describe methodology to reduce these requirements based on combining a low Mach number formulation with a local adaptive mesh refinement algorithm. The low Mach number equations, which are structurally similar to the incompressible Navier-Stokes equations, enable a larger time step while adaptive refinement reduces the number of degrees of freedom needed to represent the solution. However, integration of the low Mach number equations on adaptive grids introduces additional complexity into the discretization. We will discuss a variety of algorithmic and implementation issues that must be addressed in developing this approach and illustrate the resulting methodology on simulation of premixed, turbulent flames. You can view Dr. Bell's groups home page at: http://seesar.lbl.gov/ccse