A capturing - tracking hybrid scheme for deflagration discontinuities

A new numerical technique for the simulation of gas dynamic discontinuities in compressible flows is presented. The scheme's complexity and structure is intermediate between a higher-order shock-capturing technique and a front-tracking algorithm. It resembles a tracking scheme in that the front geometry is explicitly computed using a level set method. However, we employ the geometrical information gained in an unusual fashion. Instead of letting it define irregular part-cells wherever the front intersects a grid cell of the underlying mesh and separately balancing fluxes for these part-cells, we use the information for an accurate reconstruction of the discontinous solution in these mixed cells. The reconstructed states and again the front geometry are then used to define accurate effective numerical fluxes across those regular grid cell interfaces that are intersected by the front during the time step considered. Hence, the scheme resembles a capturing scheme in that only cell averages of conserved quantities for full cells of the underlying grid are computed. A side-effect is that the small subcell CFL problem of other conservative tracking schemes is eliminated. A disadvantage for certain applications is that the scheme is conservative with respect to the underlying grid, but that it is not separately conservative with respect to the pre- and post-front regions. If this is a crucial requirement, additional measures have to be taken.