适用于带相场机制的可压缩两相及N相流的保界相容有限体积WENO格式
Consistent and bound-preserving finite-volume WENO scheme for compressible two-/$N$-phase flows with Phase-Field mechanism
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中文总结 AI 辅助
本研究提出一种带相场机制的可压缩多相流用保界相容有限体积WENO格式，经基准测试及激波相关问题验证，可避免数值异常，适配自适应网格加密，具保界等特性。
中文摘要 AI 辅助
本研究提出一种满足相容性、守恒性、平衡性及保界性要求的有限体积WENO格式，用于处理带相场机制的可压缩多相流。该WENO格式基于由模板间相对光滑度确定的WENO权重新计算方法，以及质量与体积分数的耦合重构方法开发。开发过程中考虑了约化的相容性及体积分数求和为1的要求，当存在N（N≥1）种不同不混溶相时，数值上不会产生虚拟相、局部空隙或过填充。将该WENO格式应用于带自适应网格加密的相容守恒相场方法，开展了多种可压缩两相及N相流基准测试，以验证所提WENO格式及其带相容限制器变体的特性。最终通过激波诱导空泡溃灭及激波-容器-气泡相互作用问题，展示了所提WENO格式的能力，讨论了高阶格式保界性的必要性，并对比了不同可压缩多相流模型。
英文摘要
In the present study, we propose a consistent and bound-preserving finite-volume WENO scheme that satisfies the requirements of consistency, conservation, equilibrium, and bound preservation for compressible multiphase flows with the Phase-Field mechanism. The proposed WENO scheme is developed based on a new calculation of WENO weights determined by relative smoothness between stencils and on a coupled reconstruction of the masses and volume fractions. Consistency of reduction and volume fraction summation to unity are considered during the development so that fictitious phases, local voids, or overfilling are not produced numerically when there are $N$ ($N \geqslant 1$) different immiscible phases. The proposed WENO scheme is applied to the consistent and conservative Phase-Field method with adaptive mesh refinement enabled. Various benchmark compressible two- and $N$-phase flows are performed to verify the properties of the proposed WENO scheme as well as its variant with the consistent limiter. We finally demonstrate the capability of the proposed WENO scheme in shock-induced cavity collapse and shock-vessel-bubble interaction problems, with discussion of the necessity of bound preservation for high-order schemes and comparison of different compressible multiphase flow models.
