An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

Marcuzzi, Fabio; Cecchi, M. Morandi; Venturin, Manolo

doi:10.1016/j.matcom.2008.04.006

Cited by 5 publications

(3 citation statements)

References 10 publications

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“…We have considered only velocity fields where the principal velocities are statistically stationary, a valid assumption for strongly tidal embayments, but there is a clear extension to nonstationary flows with an adaptive regridding process. Compared with related forms of adaptive mesh refinement, such as the algorithm proposed by Marcuzzi et al in which directionality in the error field adaptively controls anisotropy in a finite element mesh, the numerical schemes with which we are concerned place much tighter constraints on the geometry of the grid. These constraints translate to more computationally intensive grid generation procedures; although our current implementation would be inefficient for frequent, global regridding steps, localized regridding in areas with nonstationary principal velocities would be feasible even with the current implementation.…”

Section: Discussionmentioning

confidence: 99%

Numerical diffusion for flow‐aligned unstructured grids with application to estuarine modeling

Holleman

Fringer

Stacey

2013

Numerical Methods in Fluids

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SUMMARYThe benefits of unstructured grids in hydrodynamic models are well understood but in many cases lead to greater numerical diffusion compared with methods available on structured grids. The flexible nature of unstructured grids, however, allows for the orientation of the grid to align locally with the dominant flow direction and thus decrease numerical diffusion. We investigate the relationship between grid alignment and diffusive errors in the context of scalar transport in a triangular, unstructured, 3‐D hydrodynamic code. Analytical results are presented for the 2‐D anisotropic numerical diffusion tensor and verified against idealized simulations. Results from two physically realistic estuarine simulations, differing only in grid alignment, show significant changes in gradients of salinity. Changes in scalar gradients are reflective of reduced numerical diffusion interacting with the complex 3‐D structure of the transporting flow. We also describe a method for utilizing flow fields from an unaligned grid to generate a flow‐aligned grid with minimal supervision. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Discussionmentioning

confidence: 99%

Numerical diffusion for flow‐aligned unstructured grids with application to estuarine modeling

Holleman

Fringer

Stacey

2013

Numerical Methods in Fluids

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“…. Now we deal with the first term on the right-hand side of (19). On each element τ , let J τ be the Jacobian of the mapping…”

Section: Superconvergence Of Fe Solutionmentioning

confidence: 99%

“…For problems exhibiting anisotropic features, e.g., internal and boundary layers, FE solutions based on anisotropic meshes can be much more effective than those based on isotropic ones. Recovery type error estimators have also been applied to this type of computation [12,14,19,25]. Numerical examples demonstrate that these estimators are still robust and reliable at the presence of 90 WEIMING CAO highly anisotropic elements [20,24].…”

Section: Introductionmentioning

confidence: 99%

Superconvergence analysis of the linear finite element method and a gradient recovery postprocessing on anisotropic meshes

Cao

2014

Math. Comp.

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For the linear finite element method based on general unstructured anisotropic meshes in two dimensions, we establish the superconvergence in energy norm of the finite element solution to the interpolation of the exact solution for elliptic problems. We also prove the superconvergence of the postprocessing process based on the global L 2 L^2 -projection of the gradient of the finite element solution. Our basic assumptions are: (i) the mesh is quasi-uniform under a Riemannian metric and (ii) each adjacent element pair forms an approximate (anisotropic) parallelogram. The analysis follows the same methodology developed by Bank and Xu in 2003 for the case of quasi-uniform meshes, and the results can be considered as an extension of their conclusion to the adaptive anisotropic meshes. Numerical examples involving both internal and boundary layers are presented in support of the theoretical analysis.

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On the superconvergence patch recovery techniques for the linear finite element approximation on anisotropic meshes

Cao

2014

Journal of Computational and Applied Mathematics

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An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information

Cited by 5 publications

References 10 publications

Numerical diffusion for flow‐aligned unstructured grids with application to estuarine modeling

Numerical diffusion for flow‐aligned unstructured grids with application to estuarine modeling

Superconvergence analysis of the linear finite element method and a gradient recovery postprocessing on anisotropic meshes

On the superconvergence patch recovery techniques for the linear finite element approximation on anisotropic meshes

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