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Computational and Applied Mathematics : Volume 36

Computational and Applied Mathematics : Volume 35

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Computational and Applied Mathematics : Volume 35, Issue 1, April 2016

High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids

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Rational cubic trigonometric Bézier curve with two shape parameters

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Computational and Applied Mathematics : Volume 34

Computational and Applied Mathematics : Volume 33

Computational and Applied Mathematics : Volume 32

High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids

Content Provider	Springer Nature Link
Author	Stolfi, Jorge Gomes, Sônia M. Castro, Douglas A.
Copyright Year	2014
Abstract	This paper considers the design of adaptive finite-volume discretizations for conservation laws. The methodology comes from the context of multiresolution representation of functions, which is based on cell averages on a hierarchy of nested grids. The refinement process is performed by the partition of each cell at a certain level into two equal child cells at the next refined level by a hyperplane perpendicular to one of the coordinate axes, which varies cyclically from level to level. The resulting dyadic grids allow the organization of the multiscale information by the same binary-tree data structure for domains in any dimension. Cell averages of neighbouring stencil cells, chosen on the subdivision direction axis, are used to approximate the cell average of the child cells in terms of a classical A. Harten prediction formula for 1D discretizations. The difference between successive refinement levels is encoded as the prediction errors (wavelet coefficients) in one of the child cells. Adaptivity is obtained by interrupting the refinement at the cells where the wavelet coefficients are sufficiently small. The efficiency of the adaptive method is analysed in applications to typical test problems in one and two space dimensions for second- and third-order schemes for the space discretization (WENO) and time integration (explicit Runge–Kutta). The results show that the adaptive solutions fit the reference finite-volume solution on the finest regular grid, and memory and CPU requirements can be considerably reduced, thanks to the efficient self-adaptive grid refinement.
Starting Page	1
Ending Page	16
Page Count	16
File Format	PDF
ISSN	01018205
Journal	Computational and Applied Mathematics
Volume Number	35
Issue Number	1
e-ISSN	18070302
Language	English
Publisher	Springer International Publishing
Publisher Date	2014-06-22
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conservation laws Wavelets Computational Mathematics and Numerical Analysis Mathematical Applications in Computer Science Multiresolution representation Dyadic grids Data structures Finite volumes Applications of Mathematics Mathematical Applications in the Physical Sciences Finite volume methods
Content Type	Text
Resource Type	Article

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Adaptive multiresolution discontinuous Galerkin schemes for conservation laws: multi-dimensional case

Behavior of Finite Volume Schemes for Hyperbolic Conservation Laws on Adaptive Redistributed Spatial Grids

On one-dimensional arbitrary high-order WENO schemes for systems of hyperbolic conservation laws

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Multiresolution Schemes for the Numerical Solution of 2-D Conservation Laws I

Well-Balanced High Order 1D Schemes on Non-uniform Grids and Entropy Residuals

Fifth Order Multi-moment WENO Schemes for Hyperbolic Conservation Laws

Fully adaptive multiresolution finite volume schemes for conservation laws (2000).

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High-order adaptive finite-volume schemes in the context of multiresolution analysis for dyadic grids

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