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

物质点法（MPM）是一种多功能的计算工具，用于模拟固体、流体、颗粒和复杂材料，在科学和工程应用中，不同流体相之间或固体与流体之间的相互作用起着重要作用。级联雪崩、凝固的熔岩、沙池和粘稠的牙膏是可以用MPM模拟的许多物理现象之一，因此它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粒子混合问题，因此在多相流体和固流相互作用现象的模拟中提出了挑战。本研究将通过实现流体与颗粒材料（沙、雪、土壤液化）以及具有固体和流体性质的复杂材料（凝胶、泡沫）的耦合来缓解这些问题，这些组合在土木工程中很常见，其中沉积、风和水侵蚀是桥梁和水坝建设的主要问题。同样，空气-雪耦合对于雪崩和火山碎屑流的建模也很重要，它可以用来做出拯救生命的预测。作为该项目一部分的算法将公开发布，以鼓励采用、复制和进一步发展。将研究整合到团队的培训、教育和对大学本科生和研究生的推广工作中，将产生更广泛的影响，这是一个研究密集型的西班牙裔服务机构。虽然MPM的混合粒子/网格框架巩固了它的优势，但它也导致了一个主要的缺点：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在一起。这限制了MPM模拟多相流体和固-流耦合现象的精度。为了减轻这一缺陷，将开发三种新的算法。首先，一种新的粒子浮力校正将允许基于密度差异的多相流体分离。其次，基于颗粒相互作用的多相流体的表面张力算法将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促进分离。第三种算法将第二种算法扩展到一般本构模型，以模拟颗粒与固体相互作用的固体-流体耦合问题，从而允许MPM用于多相流体和固体-流体耦合，而无需维护或构建单独的表面表示；值得注意的是，解混力是完全无网格的，不依赖于任何明确的边界表示，这避免了从重建表面计算精确曲率的困难。与现有的表面张力的两两公式相比，这项工作将使用状态方程的统计公式来避免除界面附近的两两相互作用，从而大大降低了计算成本，并且即使在没有有意义的表面表示的严重混合粒子配置中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，预计这种方法将自动捕获由于表面张力引起的润湿，而无需任何特殊的建模。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.