arrow
Volume 15, Issue 1
An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes

Ruo Li & Wei Zhong

Adv. Appl. Math. Mech., 15 (2023), pp. 202-243.

Published online: 2022-10

Export citation
  • Abstract

In the present study, we extend the order-preserving (OP) criterion proposed in our latest studies to the WENO-Z-type schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X, where the notation “X” is used to identify the version of the existing WENO-Z-type scheme in this paper. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.

  • AMS Subject Headings

65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-15-202, author = {Li , Ruo and Zhong , Wei}, title = {An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {202--243}, abstract = {

In the present study, we extend the order-preserving (OP) criterion proposed in our latest studies to the WENO-Z-type schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X, where the notation “X” is used to identify the version of the existing WENO-Z-type scheme in this paper. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0032}, url = {http://global-sci.org/intro/article_detail/aamm/21132.html} }
TY - JOUR T1 - An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes AU - Li , Ruo AU - Zhong , Wei JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 202 EP - 243 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0032 UR - https://global-sci.org/intro/article_detail/aamm/21132.html KW - WENO, Z-type weights, order-preserving generalized mapping, hyperbolic systems. AB -

In the present study, we extend the order-preserving (OP) criterion proposed in our latest studies to the WENO-Z-type schemes. Firstly, we innovatively present the concept of the generalized mapped WENO schemes by rewriting the Z-type weights in a uniform formula from the perspective of the mapping relation. Then, we naturally introduce the OP criterion to improve the WENO-Z-type schemes, and the resultant schemes are denoted as MOP-GMWENO-X, where the notation “X” is used to identify the version of the existing WENO-Z-type scheme in this paper. Finally, extensive numerical experiments have been conducted to demonstrate the benefits of these new schemes. We draw the conclusion that, the convergence properties of the proposed schemes are equivalent to the corresponding WENO-X schemes. The major benefit of the new schemes is that they have the capacity to achieve high resolutions and simultaneously remove spurious oscillations for long simulations. The new schemes have the additional benefit that they can greatly decrease the post-shock oscillations on solving 2D Euler problems with strong shock waves.

Ruo Li & Wei Zhong. (2022). An Extension of the Order-Preserving Mapping to the WENO-Z-Type Schemes. Advances in Applied Mathematics and Mechanics. 15 (1). 202-243. doi:10.4208/aamm.OA-2022-0032
Copy to clipboard
The citation has been copied to your clipboard