TY - JOUR
T1 - A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws
AU - Christlieb, Andrew
AU - Guo, Wei
AU - Jiang, Yan
AU - Yang, Hyoseon
N1 - Funding Information:
Andrew Christlieb was supported by AFOSR grants FA9550-12-1-0343 , FA9550-15-1-0282 , and NSF grant DMS-1418804 . Wei Guo was supported by grants NSF - DMS-1620047 and NSF - DMS-1830838 , and Hyoseon Yang was supported by the grant NRF-2015R1A5A1009350 through the National Research Foundation of Korea .
Funding Information:
Andrew Christlieb was supported by AFOSR grants FA9550-12-1-0343, FA9550-15-1-0282, and NSF grant DMS-1418804. Wei Guo was supported by grants NSF-DMS-1620047 and NSF-DMS-1830838, and Hyoseon Yang was supported by the grant NRF-2015R1A5A1009350 through the National Research Foundation of Korea.
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/3/1
Y1 - 2019/3/1
N2 - In the article [Yang et al. (2012) [37]], the authors have developed a high order moving mesh WENO method for one-dimensional (1D) hyperbolic conservation laws, which is shown to be effective in resolving shocks and other complex solution structures. In this paper, in the light of the similar moving mesh technique, we develop a novel WENO scheme with non-polynomial bases, in particular, the exponential bases to further improve the performance of WENO schemes for solving 1D conservation laws. Furthermore, we modify the original moving mesh technique by developing a new monitor function as well as a different mesh smoothing strategy. A collection of numerical examples is presented to demonstrate high order accuracy and robustness of the method in capturing smooth and non-smooth solutions including the strong δ shock arising from the weakly hyperbolic pressureless Euler equations.
AB - In the article [Yang et al. (2012) [37]], the authors have developed a high order moving mesh WENO method for one-dimensional (1D) hyperbolic conservation laws, which is shown to be effective in resolving shocks and other complex solution structures. In this paper, in the light of the similar moving mesh technique, we develop a novel WENO scheme with non-polynomial bases, in particular, the exponential bases to further improve the performance of WENO schemes for solving 1D conservation laws. Furthermore, we modify the original moving mesh technique by developing a new monitor function as well as a different mesh smoothing strategy. A collection of numerical examples is presented to demonstrate high order accuracy and robustness of the method in capturing smooth and non-smooth solutions including the strong δ shock arising from the weakly hyperbolic pressureless Euler equations.
KW - Conservation laws
KW - Exponential polynomials
KW - Finite difference
KW - Moving mesh
KW - WENO
UR - http://www.scopus.com/inward/record.url?scp=85060314611&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.12.011
DO - 10.1016/j.jcp.2018.12.011
M3 - Article
AN - SCOPUS:85060314611
VL - 380
SP - 334
EP - 354
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
ER -