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

## TL;DR

This paper introduces a high-order meshless method with adaptive refinement for fluid-structure interactions, effectively handling singularities and complex geometries to improve simulation accuracy.

## Contribution

It develops a spatially adaptive GMLS scheme with an a posteriori refinement strategy for high-fidelity fluid-structure interaction simulations.

## Key findings

- Achieves optimal convergence near singularities.
- Effectively resolves complex colloid geometries.
- Demonstrates high accuracy in fluid-structure simulations.

## 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.