TY - JOUR
T1 - An improved WENO-Z scheme with symmetry-preserving mapping
AU - Hong, Zheng
AU - Ye, Zhengyin
AU - Ye, Kun
N1 - Publisher Copyright:
© 2020, The Author(s).
PY - 2020/12
Y1 - 2020/12
N2 - Since the classical weighted essentially non-oscillatory (WENO) scheme is proposed, various improved versions have been developed, and a typical one is the WENO-Z scheme. Although better resolution is achieved, it is shown in this article that, the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation. In order to fix the problem of WENO-Z, a symmetry-preserving mapping method is proposed in this article. In the original mapping method, the weight of each sub-stencil is used to map, which is demonstrated to cause asymmetric improvement about a discontinuity. This asymmetric improvement will lead to a distorted solution, more severe with longer output time. In the symmetry-preserving mapping method, a new variable related to the smoothness indicator is selected to map, which has the same ideal value for each sub-stencil. Using the new mapping method can not only fix the distortion problem of WENO-Z, but also improve the numerical resolution. Several benchmark problems are conducted to show the improved performance of the resultant scheme.
AB - Since the classical weighted essentially non-oscillatory (WENO) scheme is proposed, various improved versions have been developed, and a typical one is the WENO-Z scheme. Although better resolution is achieved, it is shown in this article that, the result of WENO-Z scheme suffers evident distortion in the long-time simulation of the linear advection equation. In order to fix the problem of WENO-Z, a symmetry-preserving mapping method is proposed in this article. In the original mapping method, the weight of each sub-stencil is used to map, which is demonstrated to cause asymmetric improvement about a discontinuity. This asymmetric improvement will lead to a distorted solution, more severe with longer output time. In the symmetry-preserving mapping method, a new variable related to the smoothness indicator is selected to map, which has the same ideal value for each sub-stencil. Using the new mapping method can not only fix the distortion problem of WENO-Z, but also improve the numerical resolution. Several benchmark problems are conducted to show the improved performance of the resultant scheme.
KW - Hyperbolic conservation laws
KW - Mapping method
KW - Nonlinear weights
KW - WENO-Z
UR - http://www.scopus.com/inward/record.url?scp=85116095508&partnerID=8YFLogxK
U2 - 10.1186/s42774-020-00043-w
DO - 10.1186/s42774-020-00043-w
M3 - 文章
AN - SCOPUS:85116095508
SN - 2097-3462
VL - 2
JO - Advances in Aerodynamics
JF - Advances in Aerodynamics
IS - 1
M1 - 18
ER -