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

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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.