AI 中文总结
针对表面张力主导的不可压缩两相流模拟的毛细时间步长约束问题，提出带弱可压缩子循环的不可压缩求解器，将模拟速度提升8.6倍以上，验证了其在瑞利-普拉托不稳定性等问题中的有效性。
AI 中文摘要
表面张力主导的不可压缩两相流模拟因受严格的毛细时间步长约束，计算成本极高。尽管已有诸多研究提出了表面张力的时间隐式离散化方法，以允许采用更大的时间步长并加速模拟，但这些方法要么存在人工耗散问题，要么实现复杂。本文提出一种简单新颖的方法：采用带弱可压缩子循环的不可压缩求解器。该方法可放宽毛细时间步长约束，无需依赖人工耗散稳定或复杂实现，即可将模拟速度提升8.6倍以上。其核心思路是通过轻量级子步采用弱可压缩求解器辅助主不可压缩求解器，这些子步使主不可压缩求解器即使采用大时间步长，也能获得精确计算的通量和表面张力力。数值测试验证了该方法在瑞利-普拉托不稳定性、多孔介质中两相流等实际问题中的有效性，本研究为弱可压缩求解器作为不可压缩求解器的辅助工具开辟了新范式。
英文摘要
Simulations of surface-tension-dominated incompressible two-phase flows are computationally expensive due to the severe capillary time-step constraint. Although many studies have proposed time-implicit discretizations of surface tension to allow larger time-step sizes and accelerate simulations, these methods suffer from either artificial dissipation or complex implementation. Here, we propose a simple and novel approach: an incompressible solver with weakly compressible subcycling. The proposed approach relaxes the capillary time-step constraint, thereby accelerating simulations by more than $8.6\times$ without relying on artificially dissipative stabilization or requiring complex implementation. The key idea is to introduce lightweight substeps using a weakly compressible solver to assist the main incompressible solver. These substeps enable the main incompressible solver to use accurately computed fluxes and surface tension force, even with large time-step sizes. Numerical tests demonstrate the effectiveness of the proposed approach for practical problems, including the Rayleigh--Plateau instability and two-phase flows in porous media. This study paves the way for a new paradigm in which a weakly compressible solver serves as an assistant to an incompressible solver.
Comments20 pages, 14 figures
