A spatially adaptive high-order meshless method for fluid-structure interactions

Abstract

We present a scheme implementing an a posteriori refinement strategy in the context of a high-order meshless method for problems involving point singularities and fluid-solid interfaces. The generalized moving least squares (GMLS) discretization used in this work has been previously demonstrated to provide high-order compatible discretization of the Stokes and Darcy problems, offering a high-fidelity simulation tool for problems with moving boundaries. The meshless nature of the discretization is particularly attractive for adaptive h-refinement, especially when resolving the near-field aspects of variables and point singularities governing lubrication effects in fluid-structure interactions. We demonstrate that the resulting spatially adaptive GMLS method is able to achieve optimal convergence in the presence of singularities for both the div-grad and Stokes problems. Further, we present a series of simulations for flows of colloid suspensions, in which the refinement strategy efficiently achieved highly accurate solutions, particularly for colloids with complex geometries.

21 pages, 20 figures

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• A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems
• $\mathcal{H}$-HIGNN: A Scalable Graph Neural Network Framework with Hierarchical Matrix Acceleration for Simulation of Large-Scale Particulate Suspensions
• High-order simulations of isothermal flows using the local anisotropic basis function method (LABFM)
• Parallel implementation of a compatible high-order meshless method for the Stokes' equations