论文标题
Baer-Nunziato两相模型的交错投影戈诺夫型方法
A staggered-projection Godunov-type method for the Baer-Nunziato two-phase model
论文作者
论文摘要
当描述与燃烧气态的固体颗粒爆炸物中的偏齿到二次化过渡时，一个发达的两相混合模型是可压缩的Baer-Nunziato（BN）模型，其中包含固体和气相。如果该模型是由保守的戈多诺夫型方案在数值上模拟的，则可能是由孔隙界界面产生的，这可能是由于保守变量的平均过程违反了跨孔隙界面的Riemann不变性的连续性而导致的。为了抑制振荡，本文提出，通过强制执行与孔隙率跳跃的固体接触始终在气态网格细胞内，其他不连续性在气态细胞接口处出现在固定的气体交错网格上，这是在固定气体固定的交错网格上进行交错的戈多诺夫型方案。该方案基于气态细胞上Baer-Nunziato模型的标准Godunov方案，并确保与跨孔隙率跳跃的固体接触不连续性相关的Riemann不变性的连续性。当孔隙率接口在移动时，投影过程充分考虑了相关的黎曼不变性的连续性，并确保孔隙率跳到气态细胞内。这种交错的戈诺夫型方案具有很好的平衡，不仅在抑制孔隙界接口附近的虚假振荡方面具有良好的数值性能，而且还捕获了诸如冲击之类的强烈不连续性。
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.
