  A Spectral Difference (SD) algorithm on tensor-product elements which solves
the reacting compressible Navier-Stokes equations (NSE) is presented. The
classical SD algorithm is shown to be unstable when a multispecies gas where
thermodynamic properties depend on temperature and species mass fractions is
considered. In that case, a modification of the classical algorithm was
successfully employed making it stable. It uses the fact that it is better for
the multispecies case to compute primitive variables from conservative
variables at solution points and then extrapolate them at flux points rather
than extrapolating conservative variables at flux points and reconstruct
primitive variables on these points. Characteristic, wall and symmetry boundary
conditions for reactive flows in the SD framework are also introduced. They all
use the polynomial form of the variables and of the fluxes to impose the
correct boundary condition at a boundary flux point. Validation test cases on
one-dimensional and two-dimensional laminar flames have been performed using
both global chemistry and Analytically Reduced Chemistry (ARC). Results show
excellent agreement with the reference combustion code AVBP validating the
implementation of this SD method on laminar combustion.
