A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations

In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) appro...

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Bibliographic Details
Published in:Journal of computational physics 2018-12, Vol.375, p.228-239
Main Authors: Spandan, Vamsi, Lohse, Detlef, de Tullio, Marco D., Verzicco, Roberto
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Boundary conditions
Computational fluid dynamics
Computational physics
Computer simulation
Computing time
Deformation
Finite element method
Formability
Grid refinement (mathematics)
Immersed boundary method
Least squares
Mathematical analysis
Moving least squares
Multiphase flows
Simulation
Transfer functions
Uniform flow
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Summary:In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows. First, we introduce a fast moving least squares (fast-MLS) approximation technique with which we speed up the process of building transfer functions during the simulations which leads to considerable reductions in computational time. We compare the accuracy of the fast-MLS against the exact moving least squares (MLS) for the standard problem of uniform flow over a sphere. In order to overcome the restrictions set by the resolution coupling of the Lagrangian and Eulerian meshes in this particular immersed boundary method, we present an adaptive Lagrangian mesh refinement procedure that is capable of drastically reducing the number of required nodes of the basic Lagrangian mesh when the immersed boundaries can move and deform. Finally, a coarse-grained collision detection algorithm is presented which can detect collision events between several Lagrangian markers residing on separate complex geometries with minimal computational overhead. •Fast algorithms within the immersed boundary method for multiphase flows.•Fast moving least squares approximation to reduce computational cost.•Adaptive Lagrangian mesh refinement.•Coarse-grained collision detection algorithm.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.08.040