一种可压缩通用双流体模型的投影方法
A Projection Method for Compressible Generic Two-Fluid Model
AI总结：
针对可压缩双流体流动数值模拟问题，本文将单相投影方法拓展至黏性可压缩双流体场景，基于体积分数与密度乘积唯一确定压力，结合离散层稳定设计实现能量稳定，经数值测试验证有效。
摘要：
本文提出了一种适用于通用双流体模型的新型投影方法。具体而言，我们将原本针对单相变密度不可压缩与可压缩流动设计的投影方法，拓展应用于黏性可压缩双流体流动。该方法的核心思路是：单一压力$p$可由两种流体的体积分数与密度的乘积$ϕ_k ρ_k$唯一确定。此外，通过在时间离散层合理设置中间步变量，并在全离散层引入稳定项，确保了方法的稳定性。我们证明了所提数值格式的能量稳定性，并通过三个数值测试验证了其有效性。
英文摘要：
A new projection method for a generic two-fluid model is presented in this work. Specifically, we extend the projection method, originally designed for single-phase variable density incompressible and compressible flows, to viscous compressible two-fluid flows. The key idea is that the single pressure $p$ can be uniquely determined by the products of volume fractions and densities $ϕ_k ρ_k$, of the two fluids. Additionally, the stability of the method is ensured by appropriately assigning intermediate step variables at the time-discrete level and incorporating a stabilizing term at the fully discrete level. We prove the energy stability of the proposed numerical scheme, and its validity is demonstrated through three numerical tests.
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