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

• Published in: Computer methods in applied mechanics and engineering 2019-10, Vol.355 (C), p.67-93
• Main Authors: Hu, Wei, Trask, Nathaniel, Hu, Xiaozhe, Pan, Wenxiao
• Format: Article
• Language: English
• Subjects: Adaptive refinement; Discretization; ENGINEERING; Error estimator; Finite element method; Fluid dynamics; Fluid–structure interactions; Generalized moving least squares; Lubrication; Meshless method; Meshless methods; Singularities; Stokes equation
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.06.009

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. •An a posteriori adaptive refinement strategy is proposed in the context of generalized moving least squares (GMLS), a compatible high-order meshless method.•The resulting adaptive GMLS method can efficiently resolve point singularities and capture lubrication effects in fluid–structure interactions and achieve optimal convergence.•Simulations for flows of colloid suspensions are presented, in which the adaptive GMLS efficiently achieves highly accurate solutions, particularly for colloids with complex geometries.