  In this paper we present a fourth-order in space and time block-structured
adaptive mesh refinement algorithm for the compressible multicomponent reacting
Navier-Stokes equations. The algorithm uses a finite volume approach that
incorporates a fourth-order discretization of the convective terms. The time
stepping algorithm is based on a multi-level spectral deferred corrections
method that enables explicit treatment of advection and diffusion coupled with
an implicit treatment of reactions. The temporal scheme is embedded in a
block-structured adaptive mesh refinement algorithm that includes subcycling in
time with spectral deferred correction sweeps applied on levels. Here we
present the details of the multi-level scheme paying particular attention to
the treatment of coarse-fine boundaries required to maintain fourth-order
accuracy in time. We then demonstrate the convergence properties of the
algorithm on several test cases including both nonreacting and reacting flows.
Finally we present simulations of a vitiated dimethyl ether jet in 2D and a
turbulent hydrogen jet in 3D, both with detailed kinetics and transport.
