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.

当描述固体颗粒炸药与燃烧气态产物混合时的爆燃-爆轰过渡时，一个发达的两相混合物模型是包含固相和气相的可压缩的Baer-Nunziato（BN）模型。由于该模型是通过保守的Godunov型方案进行数值模拟的，因此虚假振荡很可能是由孔隙界面产生的，并且可能是由保守变量的平均过程产生的，该过程违反了跨孔隙界面的Riemann不变量的连续性。为了减少数值振荡，本文提出了在固定的气固交错网格上的交错投影Godunov型方案，通过强迫具有孔隙率跳跃的压实波总是在气态网格单元内部并且在气态单元界面处出现其他不连续性。该方案基于用于气室Baer-Nunziato模型的标准Godunov方案，并保证了与跨孔隙跳跃的压实波相关的Riemann不变量的连续性。当孔隙界面移动时，投影过程会充分考虑相关联的黎曼不变量的连续性，并确保孔隙跳跃保留在气态细胞内。此外，应用广义黎曼问题（GRP）求解器，不仅可以达到二阶精度，减少数值振荡，而且还可以保证所得方案的均衡性能。投影过程充分考虑了相关黎曼不变量的连续性，并确保气孔内部保留孔隙率跳跃。此外，应用广义黎曼问题（GRP）求解器，不仅可以达到二阶精度，减少数值振荡，而且还可以保证所得方案的均衡性能。投影过程充分考虑了相关黎曼不变量的连续性，并确保气孔内部保留孔隙率跳跃。此外，应用广义黎曼问题（GRP）求解器，不仅可以达到二阶精度，减少数值振荡，而且还可以保证所得方案的均衡性能。