A CAPTURING-TRACKING HYBRID SCHEME FOR DEFLAGRATION DISCONTINUITIES

A new numerical technique for the simulation of gas dynamic discontinu ities in compressible Rows is presented. The scheme's complexity and s tructure is intermediate between a higher-order shock-capturing techni que and a front-tracking algorithm. It resembles a tracking scheme in that the front geometry is explicitly computed using a level set metho d. However, we employ the geometrical information gained in an unusual fashion. Instead of letting it define irregular part-cells wherever t he front intersects a grid cell of the underlying mesh and separately balancing fluxes for these part-cells, we use the information for an a ccurate reconstruction of the discontinous solution in these mixed cel ls. The reconstructed states and again the front geometry are then use d to define accurate effective numerical fluxes across those regular g rid cell interfaces that are intersected by the front during the time step considered. Hence, the scheme resembles a capturing scheme in tha t only cell averages of conserved quantities for full cells of the und erlying grid are computed. A side-effect is that the small subcell CFL problem of other conservative tracking schemes is eliminated. A disad vantage for certain applications is that the scheme is conservative wi th respect to the underlying grid, but that it is not separately conse rvative with respect to the pre- and post-front regions. If this is a crucial requirement, additional measures have to be taken. The scheme has been developed originally for deflagration waves, but with minor m odifications it may also be used to follow shocks and detonation waves .