Spectral distributed Lagrange multiplier method: algorithm and benchmark tests

We extend the formulation of the distributed Lagrange multiplier (DLM) approach for particulate flows to high-order methods within the spectral/ hp element framework. We implement the rigid-body motion constraint inside the particle via a penalty method. The high-order DLM method demonstrates spectr...

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Bibliographic Details
Published in:Journal of computational physics Vol. 195; no. 2; pp. 695 - 717
Main Authors: Dong, Suchuan, Liu, Dong, Maxey, Martin R, Karniadakis, George Em
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.04.2004
Elsevier
Subjects:
Computational techniques
Exact sciences and technology
Mathematical methods in physics
Physics
Lagrange multiplier
Algorithms
Discretization
Digital simulation
Convergence rate
Numerical method
Calculation
Lagrangian method
Calculation methods
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:We extend the formulation of the distributed Lagrange multiplier (DLM) approach for particulate flows to high-order methods within the spectral/ hp element framework. We implement the rigid-body motion constraint inside the particle via a penalty method. The high-order DLM method demonstrates spectral convergence rate, i.e. discretization errors decrease exponentially as the order of spectral polynomials increases. We provide detailed comparisons between the spectral DLM method, direct numerical simulations, and the force coupling method for a number of 2D and 3D benchmark flow problems. We also validate the spectral DLM method with available experimental data for a transient problem. The new DLM method can potentially be very effective in many-moving body problems, where a smaller number of grid points is required in comparison with low-order methods.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2003.10.016