A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws

Fei Teng; Li Yuan; Tao TANG

doi:10.1007/s10915-010-9407-9

A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws

Fei Teng, Li Yuan^*, Tao TANG

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

6 Citations (Scopus)

Abstract

In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational cost by 20-40%, especially for problems with large fraction of constant regions.

Original language	English
Pages (from-to)	359-378
Number of pages	20
Journal	Journal of Scientific Computing
Volume	46
Issue number	3
DOIs	https://doi.org/10.1007/s10915-010-9407-9
Publication status	Published - Mar 2011

Scopus Subject Areas

Software
Theoretical Computer Science
Numerical Analysis
General Engineering
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

User-Defined Keywords

Conservation law
Finite volume WENO method
Multi-dimension
Speed-up strategy

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10.1007/s10915-010-9407-9

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title = "A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws",

abstract = "In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational cost by 20-40%, especially for problems with large fraction of constant regions.",

keywords = "Conservation law, Finite volume WENO method, Multi-dimension, Speed-up strategy",

author = "Fei Teng and Li Yuan and Tao TANG",

note = "Funding Information: Fig. 11 Density contours at t = 0.25 and z = 0 for explosion test in 3D with 50 × 50 × 50 grids, CFL = 0.15, and local Lax-Friedrichs flux Fig. 12 Pressure contours at t = 0.25 and z = 0 for explosion test in 3D with 50 × 50 × 50 grids, CFL = 0.15, and local Lax-Friedrichs flux Acknowledgements This work is supported by Natural Science Foundation of China (10531080, 10729101, 10972230) and state key program for developing basic sciences (2005CB321703, 2010CB731505).",

year = "2011",

month = mar,

doi = "10.1007/s10915-010-9407-9",

language = "English",

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T1 - A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws

AU - Teng, Fei

AU - Yuan, Li

AU - TANG, Tao

N1 - Funding Information: Fig. 11 Density contours at t = 0.25 and z = 0 for explosion test in 3D with 50 × 50 × 50 grids, CFL = 0.15, and local Lax-Friedrichs flux Fig. 12 Pressure contours at t = 0.25 and z = 0 for explosion test in 3D with 50 × 50 × 50 grids, CFL = 0.15, and local Lax-Friedrichs flux Acknowledgements This work is supported by Natural Science Foundation of China (10531080, 10729101, 10972230) and state key program for developing basic sciences (2005CB321703, 2010CB731505).

PY - 2011/3

Y1 - 2011/3

N2 - In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational cost by 20-40%, especially for problems with large fraction of constant regions.

AB - In this paper, a speed-up strategy for finite volume WENO schemes is developed for solving hyperbolic conservation laws. It adopts p-adaptive like reconstruction, which automatically adjusts from fifth order WENO reconstruction to first order constant reconstruction when nearly constant solutions are detected by the undivided differences. The corresponding order of accuracy for the solutions is shown to be the same as obtained by original WENO schemes. The strategy is implemented with both WENO and mapped WENO schemes. Numerical examples in different space dimensions show that the strategy can reduce the computational cost by 20-40%, especially for problems with large fraction of constant regions.

KW - Conservation law

KW - Finite volume WENO method

KW - Multi-dimension

KW - Speed-up strategy

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U2 - 10.1007/s10915-010-9407-9

DO - 10.1007/s10915-010-9407-9

M3 - Journal article

AN - SCOPUS:79751533248

SN - 0885-7474

VL - 46

SP - 359

EP - 378

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -

A speed-up strategy for finite volume WENO schemes for hyperbolic conservation laws

Abstract

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