Local defect correction with different grid types

Nefedov, V.V.; Mattheij, R.M.M.

doi:10.1002/num.10018

Cited by 11 publications

(12 citation statements)

References 6 publications

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“…LDC is studied in combination with finite element discretizations in [45]. Nefedov and Mattheij [34] consider the LDC method for the case where the global coarse and local fine grids are of a different nature. Whereas most authors consider a composite grid built up of two or more Cartesian grids, Nefedov and Mattheij use a polar grid for the local area.…”

Section: Introductionmentioning

confidence: 99%

An adaptive multilevel local defect correction technique with application to combustion

Anthonissen¹,

Bennett²,

Smooke³

2005

Combustion Theory and Modelling

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The standard local defect correction (LDC) method has been extended to include multilevel adaptive gridding, domain decomposition, and regridding. The domain decomposition algorithm provides a natural route for parallelization by employing many small tensor-product grids, rather than a single large unstructured grid; this algorithm can greatly reduce memory usage. The above properties are illustrated by successfully applying the new algorithm to a simple heat transfer problem with an analytical solution, and by subsequently solving the more complex problem of an axisymmetric laminar Bunsen flame with one-step chemistry. The simulation data show excellent agreement with results previously published in the literature.

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Section: Introductionmentioning

confidence: 99%

An adaptive multilevel local defect correction technique with application to combustion

Anthonissen¹,

Bennett²,

Smooke³

2005

Combustion Theory and Modelling

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“…polar grids instead of Cartesian; cf. [17]); solving a different system of equations on different grids (e.g. analytical expressions or equilibrium assumptions).…”

Section: Two-grid Ldc Algorithm With Area Of Refinement Chosen a Priomentioning

confidence: 99%

“…So-called high order compact difference schemes can be used in an LDC technique too [16]. In [9,17] LDC is studied with different grid types. The method is successfully applied to a combustion problem in [1].…”

Section: Introductionmentioning

confidence: 99%

Local defect correction in numerical simulation of surface remelting

Anthonissen

2007

International Journal of Computer Mathematics

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We study the efficient numerical simulation of laser surface remelting, a process to improve the surface quality of steel components. To this end we use adaptive grids, which are well-suited for problems with moving heat sources. To account for the local high activity due to the heat source, we introduce local uniform grids and couple the solutions on the global coarse and local fine grids using local defect correction (LDC). LDC is based on simple data structures and simple discretization stencils on uniform or tensor-product grids.

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“…In [4] the LDC method is combined with multi-level adaptive grid refinement, with an application to laminar flame simulation. Finally in [6] and [7] it is shown how different kinds of grids, namely a global rectangular and a local cylindrical, can be coupled by LDC and applied to the study of viscous flows.…”

Section: Introductionmentioning

confidence: 99%

Local defect correction with slanting grids

Graziadei

Mattheij

Boonkkamp

2003

Numerical Methods Partial

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The local defect correction (LDC) method is used to solve a convection‐diffusion‐reaction problem that contains a high‐activity region in a relatively small part of the domain. The improvement of the solution on a coarse grid is obtained by introducing a correction term computed from a local fine‐grid solution. This article studies problems where the high‐activity region is covered with a rectangular fine grid not aligned with the axes of the global domain. This study shows that the resulting method is less expensive than both a uniform refinement and tensor product grid method. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 1–17, 2004.

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Local defect correction with different grid types

Cited by 11 publications

References 6 publications

An adaptive multilevel local defect correction technique with application to combustion

An adaptive multilevel local defect correction technique with application to combustion

Local defect correction in numerical simulation of surface remelting

Local defect correction with slanting grids

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