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  1. Material in HED regimes are at very high pressures and temperatures but can often still be modeled in the plasma-fluid approximation. Historically HED regimes were created using large laser/ion- beam drivers heating solid targets. Exciting data was obtained from these single shot experiments. In recent years there has been a shift to obtain HED related data from a large number of shots by using high-repetition-rate drivers. For high-repetition-rate experiments a series of droplet targets are often used to have a fresh target/droplet for each shot. However, one must make sure that target debris from the previous shot does not degrade the target for subsequent shots. This is a challenging CFD problem as one needs to model the initial dynamics of the heated droplet and the subsequent interaction with the following droplets. We use the CFD modeling code PISALE to study this complex problem. We discuss results for liquid hydrogen droplets heated by an x-ray free electron laser (XFEL). We first show 2D results for single heated droplet then 3D results for a heated droplet interacting with two unheated droplets. 
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  2. Particulate matter and small debris present in the atmosphere are known to cause substantial progressive damage to leading edges and control surfaces on hypersonic vehicles. This study seeks to predict the material responses (mechanical and thermal) to high-speed, small particle impact loading during hypersonic flight. To address such challenges, a multi-material fluid-based approach for modeling problems in this regime is examined. This method combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR) and multi- zone physics. The parameter regime of particles (2-5 μm) impacting a material surface at high speeds (125 - 600 ms−1) is investigated. 
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  3. The solution of partial differential equations (PDEs) on modern high performance computing (HPC) platforms is essential to the continued success of groundwater flow and transport modeling in Pacific islands where complex regional groundwater flow is governed by highly heterogeneous volcanic rocks and dynamic interaction between freshwater and seawater. For accurate simulations of complex groundwater flow processes in the Hawaiian islands, the PISALE (Pacific Island Structured-AMR with ALE) software has been developed to offer an innovative combination of advanced mathematical techniques such as arbitrary Lagrangian-Eulerian method (ALE) and Adaptive Mesh Refinement (AMR). The software uses parallel programming models to accelerate the time to solution and dynamically adapt the grids using AMR. This allows for the solution of equations that can reproduce the sharp freshwater-seawater interface in large-scale coast aquifers. In this work, we summarize our ongoing efforts to create a publicly available sustainable branch of the software focused on the groundwater problem. The island-scale numerical groundwater flow modeling will play an important role in predicting the sustainable yields and potential contaminant transport for the volcanic aquifer systems and planning groundwater resources management. 
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  4. We discuss recent advances in a Computational Fluid Dynamics (CFD) framework that uses a combination of of Arbitrary Langrangian Eulerian (ALE) Dynamics and Adaptive Mesh Refinement (AMR). We describe updates and on-going work on the framework that allow for build portability on generic HPC (High Performance Computing) platforms. We also describe some of the more advanced algorithms that are available in the framework such as those which model surface tension effects in two and three dimensions. We introduce a new method for curvature and normal vector calculation in 2D, which we call the method of osculating circles. We benchmark this method and compare with other other volume of ŕuid (VOF) approaches to simulating surface tension effects. We predict how these algorithms will scale on these latest platforms such as the new Perlmutter system at NERSC which is a HPE Cray EX supercomputer with both GPU-accelerated and CPU-only nodes. We discuss the application of surface tension models to the interaction of a hydrogen droplet heated by an x-ray free electron laser with another hydrogen droplet. 
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