A staggered-projection Godunov-type method for the Baer-Nunziato two-phase model

Abstract

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 of flows containing solid and gas phases. As this model is numerically simulated by a conservative Godunov-type scheme, spurious oscillations are likely to generate from porosity interfaces, and may result from the average process of conservative variables that violates the continuity of Riemann invariants across porosity interfaces. In order to reduce numerical oscillations, this paper proposes a staggered-projection Godunov-type scheme over a fixed gas-solid staggered grid, by enforcing that compaction waves with porosity jumps are always inside gaseous grid cells and other discontinuities appear at gaseous cell interfaces. The 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 compaction waves across porosity jumps. While porosity interfaces are moving, a projection process fully takes into account the continuity of associated Riemann invariants and ensures that porosity jumps remain inside gaseous cells. Furthermore, the generalized Riemann problem (GRP) solver is applied, not only to achieve second-order accuracy, reduce numerical oscillations, but guarantees the well-balanced property of the resulting scheme as well.