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A Novel Multi-Dimensional Limiter for High-Order Finite Volume Methods on Unstructured Grids

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Waves Hyperbolic equations and systems

Published online by Cambridge University Press:  31 October 2017

Yilang Liu ,
Weiwei Zhang  and
Chunna Li
Yilang Liu*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, No. 127 Youyi West Road, Xi'an 710072, China
Weiwei Zhang*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, No. 127 Youyi West Road, Xi'an 710072, China
Chunna Li*
Affiliation:
National Key Laboratory of Aerospace Flight Dynamics, School of Astronautics, Northwestern Polytechnical University, No. 127 Youyi West Road, Xi'an 710072, China
*
*Corresponding author. Email addresses:aeroelastic@nwpu.edu.cn(W.W. Zhang), liuyilang1212112@163.com(Y. L. Liu), chunnali@nwpu.edu.cn(C. N. Li)
*Corresponding author. Email addresses:aeroelastic@nwpu.edu.cn(W.W. Zhang), liuyilang1212112@163.com(Y. L. Liu), chunnali@nwpu.edu.cn(C. N. Li)
*Corresponding author. Email addresses:aeroelastic@nwpu.edu.cn(W.W. Zhang), liuyilang1212112@163.com(Y. L. Liu), chunnali@nwpu.edu.cn(C. N. Li)
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Abstract

This paper proposes a novel distance derivative weighted ENO (DDWENO) limiter based on fixed reconstruction stencil and applies it to the second- and highorder finite volume method on unstructured grids. We choose the standard deviation coefficients of the flow variables as the smooth indicators by using the k-exact reconstruction method, and obtain the limited derivatives of the flow variables by weighting all derivatives of each cell according to smoothness. Furthermore, an additional weighting coefficient related to distance is introduced to emphasize the contribution of the central cell in smooth regions. The developed limiter, combining the advantages of the slope limiters and WENO-type limiters, can achieve the similar effect of WENO schemes in the fixed stencil with high computational efficiency. The numerical cases demonstrate that the DDWENO limiter can preserve the numerical accuracy in smooth regions, and capture the shock waves clearly and steeply as well.

Keywords

High-order finite volume methodunstructured gridsDDWENO limitershock waves

MSC classification

Secondary: 35L25: Higher-order hyperbolic equations 65M08: Finite volume methods 65M12: Stability and convergence of numerical methods 74J40: Shocks and related discontinuities
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 5 , November 2017 , pp. 1385 - 1412
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

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