We present a novel implicit porous flow solver using SPH, which maintains fluid incompressibility and is able to model a wide range of scenarios, driven by strongly coupled solid-fluid interaction forces. Many previous SPH porous flow methods reduce particle volumes as they transition across the solid-fluid interface, resulting in significant stability issues. We instead allow fluid and solid to overlap by deriving a new density estimation. This further allows us to extend SPH pressure solvers to take local porosity into account and results in strict enforcement of incompressibility. As a result, we can simulate porous flow using physically consistent pressure forces between fluid and solid. In contrast to previous SPH porous flow methods, which use explicit forces for internal fluid flow, we employ implicit non-pressure forces. These we solve as a linear system and strongly couple with fluid viscosity and solid elasticity. We capture the most common effects observed in porous flow, namely drag, buoyancy and capillary action due to adhesion. To achieve elastic behavior change based on local fluid saturation, such as bloating or softening, we propose an extension to the elasticity model. We demonstrate the efficacy of our model with various simulations that showcase the different aspects of porous flow behavior. To summarize, our system of strongly coupled non-pressure forces and enforced incompressibility across overlapping phases allows us to naturally model and stably simulate complex porous interactions.

翻译：本文提出了一种新颖的基于光滑粒子流体动力学（SPH）的隐式多孔流动求解器，该求解器能够保持流体的不可压缩性，并能够模拟由强耦合固-液相互作用力驱动的多种场景。以往许多SPH多孔流动方法在粒子跨越固-液界面时减少其体积，导致显著的稳定性问题。我们通过推导新的密度估计方法，允许流体与固体发生重叠。这进一步使我们能够扩展SPH压力求解器以考虑局部孔隙率，从而严格保证不可压缩性。因此，我们能够使用流体与固体之间物理一致的压力力来模拟多孔流动。与以往使用显式力处理内部流体流动的SPH多孔流动方法不同，我们采用隐式非压力力。我们将这些力作为线性系统求解，并与流体粘性和固体弹性强耦合。我们捕捉了多孔流动中最常见的效应，即由粘附引起的阻力、浮力和毛细作用。为了实现基于局部流体饱和度（如膨胀或软化）的弹性行为变化，我们提出了弹性模型的扩展。我们通过多种模拟展示了模型的有效性，这些模拟展现了多孔流动行为的不同方面。总之，我们提出的强耦合非压力力系统及在重叠相中强制实施的不可压缩性，使我们能够自然地建模并稳定地模拟复杂的多孔相互作用。