  When describing the deflagration-to-detonation transition in solid granular
explosives mixed with gaseous products of combustion, a well-developed
two-phase mixture model is the compressible Baer-Nunziato (BN) model,
containing solid and gas phases. If this model is numerically simulated by a
conservative Godunov-type scheme, spurious oscillations are likely to generate
from porosity interfaces, which may result from the average process of
conservative variables that violates the continuity of Riemann invariants
across porosity interfaces. In order to suppress the oscillations, this paper
proposes a staggered-projection Godunov-type scheme over a fixed gas-solid
staggered grid, by enforcing that solid contacts with porosity jumps are always
inside gaseous grid cells and other discontinuities appear at gaseous cell
interfaces. This scheme is based on a standard Godunov scheme for the
Baer-Nunziato model on gaseous cells and guarantees the continuity of the
Riemann invariants associated with the solid contact discontinuities across
porosity jumps. While porosity interfaces are moving, a projection process
fully takes into account the continuity of associated Riemann invariants and
ensure that porosity jumps remain inside gaseous cells. This
staggered-projection Godunov-type scheme is well-balanced with good numerical
performance not only on suppressing spurious oscillations near porosity
interfaces but also capturing strong discontinuities such as shocks.
