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

Computer Methods in Applied Mechanics and Engineering

Hu, Wei; Trask, Nathaniel A.; Hu, Xiaozhe; Pan, Wenxiao

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.

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TYPE Journal Article YEAR 2019
ScopusOSTIDOI

Compatible Particle Discretizations. Final LDRD Report

Bochev, Pavel B.; Bosler, Peter A.; Kuberry, Paul A.; Perego, Mauro P.; Peterson, Kara J.; Trask, Nathaniel A.

This report summarizes the work performed under a three year LDRD project aiming to develop mathematical and software foundations for compatible meshfree and particle discretizations. We review major technical accomplishments and project metrics such as publications, conference and colloquia presentations and organization of special sessions and minisimposia. The report concludes with a brief summary of ongoing projects and collaborations that utilize the products of this work.

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TYPE SAND Report YEAR 2019
OSTIDOI

An asymptotically compatible meshfree quadrature rule for nonlocal problems with applications to peridynamics

Computer Methods in Applied Mechanics and Engineering

Trask, Nathaniel A.; You, Huaiqian; Yu, Yue; Parks, Michael L.

We present a meshfree quadrature rule for compactly supported nonlocal integro-differential equations (IDEs) with radial kernels. We apply this rule to develop a meshfree discretization of a peridynamic solid mechanics model that requires no background mesh. Existing discretizations of peridynamic models have been shown to exhibit a lack of asymptotic compatibility to the corresponding linearly elastic local solution. By posing the quadrature rule as an equality constrained least squares problem, we obtain asymptotically compatible convergence by introducing polynomial reproduction constraints. Our approach naturally handles traction-free conditions, surface effects, and damage modeling for both static and dynamic problems. We demonstrate high-order convergence to the local theory by comparing to manufactured solutions and to cases with crack singularities for which an analytic solution is available. Finally, we verify the applicability of the approach to realistic problems by reproducing high-velocity impact results from the Kalthoff–Winkler experiments.

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TYPE Journal Article YEAR 2019
ScopusOSTIDOI
Results 51–100 of 100
Results 51–100 of 100