CHS: Small: Novel methods for material point method simulations of multiphase fluids

材料点法(MPM)是一种通用的计算工具，用于模拟科学和工程应用中的固体、流体、颗粒和复杂材料，在这些应用中，不同流体之间或固体与流体之间的相互作用起着重要作用。层叠的雪崩、凝固的熔岩、沙池和黏糊糊的牙膏是许多可以用MPM模拟的物理现象，因此被广泛用于工程应用和基于物理的动画。但该方法存在非物理颗粒混合问题，对多相流体和固液相互作用现象的模拟提出了挑战。这项研究将通过将流体与颗粒材料(沙、雪、土壤液化)以及表现出类固体和类流体特性的复合材料(凝胶、泡沫)相耦合来缓解这些问题，这些组合在土木工程中很常见，因为在土木工程中，桥梁和大坝建设主要考虑的是沉积和风、水侵蚀。同样，空气-雪耦合对于模拟雪崩和火山碎屑流也很重要，在那里它可以用来做出拯救生命的预测。作为该项目的一部分产生的算法将被公开发布，以鼓励采用、复制和进一步进步。其他广泛的影响将来自于将研究整合到团队对其大学本科生和研究生的培训、教育和推广工作中，这是一所研究密集型拉美裔服务机构。尽管MPM的混合粒子/网格框架支撑了其优势，但它也导致了一个重大缺点：来自不同材料的粒子倾向于以物理上不可能的方式混合和粘合在一起。这限制了MPM在模拟多相流体和固液耦合现象时的精度。为了缓解这一不足，将开发三种新的算法。首先，一种新的对颗粒的浮力修正将允许基于密度差异的多相流体的混合。其次，基于颗粒相互作用的多相流体表面张力算法通过将材料的本构模型与不同材料之间的相互作用力解耦来鼓励混合。第三种算法将第二种算法扩展到一般本构模型，模拟颗粒与固体相互作用的固流耦合问题，从而允许MPM用于多相流体和固流耦合，而不需要维护或构造单独的表面表示；值得注意的是，分解力是纯无网格的，不依赖于边界的任何显式表示，这避免了从重建表面计算精确曲率的困难。与现有的表面张力力成对公式相比，这项工作将使用状态方程的统计公式来避免除界面附近以外的两两相互作用，从而大大降低计算成本，并允许即使在没有有意义的表面表示的严重混合粒子构型下也能获得准确的结果，这是现有公式在不违反守恒定律的情况下无法做到的。此外，预计该方法将自动捕获由于表面张力而导致的湿润，而无需任何特殊建模。该奖项反映了NSF的法定使命，并已通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The material point method (MPM) is a versatile computational tool for simulating solids, fluids, granular and complex materials in scientific and engineering applications where interactions between separate fluid phases, or between solids and fluids, play an important role. Cascading avalanches, solidifying lava, sandy pools, and gooey toothpaste are among the many physical phenomena that can be simulated with MPM, which is therefore used extensively for engineering applications and physics-based animation. But the method suffers from problems of nonphysical particle mixing and thus presents challenges in the simulation of multiphase fluids and solid-fluid interaction phenomena. This research will alleviate these issues by enabling the coupling of fluids with granular materials (sand, snow, soil liquefaction) as well as complex materials that exhibit solid-like and fluid-like properties (gels, foams), combinations that are common in civil engineering where sedimentation and wind and water erosion are major concerns for bridge and dam constructions. Similarly, air-snow coupling is important for modeling avalanches and pyroclastic flows, where it can be used to make life-saving predictions. The algorithms produced as part of this project will be publicly released to encourage adoption, reproduction, and further advancements. Additional broad impacts will derive from integration of the research into the team's training, educational, and outreach efforts to students at both the undergraduate and graduate levels in their university, which is a research-intensive Hispanic Serving Institution.While the hybrid particle/grid framework of MPM underpins its strengths, it also leads to a major downside: particles from different materials tend to mix and stick together in ways that are physically impossible. This limits the accuracy of MPM in simulating multiphase fluid and solid-fluid coupling phenomena. To alleviate this deficiency, three novel algorithms will be developed. First, a novel buoyancy force correction on particles will allow for unmixing of multiphase fluids based on density differences. Second, a surface tension algorithm for multiphase fluids based on particle interactions will encourage unmixing by decoupling constitutive models of materials from interaction forces between different materials. The third algorithm will extend the second to general constitutive models, to simulate problems of solid-fluid coupling where particles interact with solids, thereby allowing MPM to be used for multiphase fluids and solid-fluid coupling without the need to maintain or construct a separate surface representation; notably, the unmixing forces are purely meshless and do not rely on any explicit representation for the boundary, which avoids the difficulties of computing accurate curvature from the reconstructed surface. Compared with existing pairwise formulations of surface tension forces, this work will use a statistical formulation for an equation of state to avoid pairwise interactions except near the interface, thereby drastically reducing the computational cost and allowing accurate results to be obtained even with heavily mixed particle configurations where no meaningful surface representation exists, something existing formulations cannot do without violating conservation laws. It is furthermore expected that this approach will automatically capture wetting due to surface tension without any special modeling.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.