Theoretical and Numerical Structure for Reacting Shock Waves

Several remarkable theoretical and computational properties of reacting shock waves are both documented and analyzed. In particular, for sufficiently small heat release or large reaction rate, we demonstrate that the reacting compressible Navier–Stokes equations have dynamically stable weak detonations which occur in bifurcating wave patterns from strong detonation initial data. In the reported calculations, an increase in reaction rate by a factor of 5 is sufficient to create the bifurcation from a spiked nearly Z-N-D detonation to the wave pattern with a precursor weak detonation. The numerical schemes used in the calculations are fractional step methods based on the use of a second order Godunov method in the inviscid hydrodynamic sweep; on sufficiently coarse meshes in inviscid calculations, these fractional step schemes exhibit qualitatively similar but purely numerical bifurcating wave patterns with numerical weak detonations. We explain this computational phenomenon theoretically through a new class of nonphysical discrete travelling waves for the difference scheme which are numerical weak detonations. The use of simplified model equations both to predict and analyze the theoretical and numerical phenomena is emphasized.