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1. Simulating hindered grain boundary diffusion using the smoothed boundary method

   https://doi.org/10.1088/1361-651X/ad4d0b  

   Hanson, Erik; Andrews, W_Beck; Powers, Max; Jenkins, Kaila_G; Thornton, Katsuyo (June 2024, Modelling and Simulation in Materials Science and Engineering)

   Abstract Grain boundaries can greatly affect the transport properties of polycrystalline materials, particularly when the grain size approaches the nanoscale. While grain boundaries often enhance diffusion by providing a fast pathway for chemical transport, some material systems, such as those of solid oxide fuel cells and battery cathode particles, exhibit the opposite behavior, where grain boundaries act to hinder diffusion. To facilitate the study of systems with hindered grain boundary diffusion, we propose a model that utilizes the smoothed boundary method to simulate the dynamic concentration evolution in polycrystalline systems. The model employs domain parameters with diffuse interfaces to describe the grains, thereby enabling solutions with explicit consideration of their complex geometries. The intrinsic error arising from the diffuse interface approach employed in our proposed model is explored by comparing the results against a sharp interface model for a variety of parameter sets. Finally, two case studies are considered to demonstrate potential applications of the model. First, a nanocrystalline yttria-stabilized zirconia solid oxide fuel cell system is investigated, and the effective diffusivities are extracted from the simulation results and are compared to the values obtained through mean-field approximations. Second, the concentration evolution during lithiation of a polycrystalline battery cathode particle is simulated to demonstrate the method’s capability. 

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2. Self-similar diffuse boundary method for phase boundary driven flow

   https://doi.org/10.1063/5.0107739  

   Schmidt, Emma M.; Quinlan, J. Matt; Runnels, Brandon (November 2022, Physics of Fluids)

   Interactions between an evolving solid and inviscid flow can result in substantial computational complexity, particularly in circumstances involving varied boundary conditions between the solid and fluid phases. Examples of such interactions include melting, sublimation, and deflagration, all of which exhibit bidirectional coupling, mass/heat transfer, and topological change of the solid–fluid interface. The diffuse interface method is a powerful technique that has been used to describe a wide range of solid-phase interface-driven phenomena. The implicit treatment of the interface eliminates the need for cumbersome interface tracking, and advances in adaptive mesh refinement have provided a way to sufficiently resolve diffuse interfaces without excessive computational cost. However, the general scale-invariant coupling of these techniques to flow solvers has been relatively unexplored. In this work, a robust method is presented for treating diffuse solid–fluid interfaces with arbitrary boundary conditions. Source terms defined over the diffuse region mimic boundary conditions at the solid–fluid interface, and it is demonstrated that the diffuse length scale has no adverse effects. To show the efficacy of the method, a one-dimensional implementation is introduced and tested for three types of boundaries: mass flux through the boundary, a moving boundary, and passive interaction of the boundary with an incident acoustic wave. Two-dimensional results are presented as well these demonstrate expected behavior in all cases. Convergence analysis is also performed and compared against the sharp-interface solution, and linear convergence is observed. This method lays the groundwork for the extension to viscous flow and the solution of problems involving time-varying mass-flux boundaries. 

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3. The volume-filtering immersed boundary method

   https://doi.org/10.1016/j.jcp.2023.112136  

   Dave, Himanshu; Herrmann, Marcus; Kasbaoui, M. Houssem (August 2023, Journal of Computational Physics)
4. Dataset: Simulating Hindered Grain Boundary Diffusion Using the Smoothed Boundary Method

   https://doi.org/10.13011/m3-0mxz-xd55  

   Hanson, Erik; Andrews, W Beck; Powers, Max; Jenkins, Kaila G; Thornton, Katsuyo (January 2024, Materials Commons)

   Data associated with the article "Simulating Hindered Grain Boundary Diffusion Using the Smoothed Boundary Method" [1]. 1. Hanson, E., Andrews, W. B., Powers, M., Jenkins, K. G., & Thornton, K. (2024). Simulating hindered grain boundary diffusion using the smoothed boundary method. Modelling and Simulation in Materials Science and Engineering, 32(5), 055027. 

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5. Linearized boundary control method for an acoustic inverse boundary value problem

   https://doi.org/10.1088/1361-6420/ac91eb  

   Oksanen, Lauri; Yang, Tianyu; Yang, Yang (October 2022, Inverse Problems)

   Abstract We develop a linearized boundary control method for the inverse boundary value problem of determining a potential in the acoustic wave equation from the Neumann-to-Dirichlet map. When the linearization is at the zero potential, we derive a reconstruction formula based on the boundary control method and prove that it is of Lipschitz-type stability. When the linearization is at a nonzero potential, we prove that the problem is of Hölder-type stability in two and higher dimensions. The proposed reconstruction formula is implemented and evaluated using several numerical experiments to validate its feasibility. 

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