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Volume 30, Issue 5
A Modified Adaptive Improved Mapped WENO Method

Ruo Li & Wei Zhong

DOI: 10.4208/cicp.OA-2021-0057

Commun. Comput. Phys., 30 (2021), pp. 1545-1588.

Published online: 2021-10

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  • Abstract

We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergence rates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. It produces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.

  • Keywords

WENO schemes, adaptive mapping functions, hyperbolic conservation laws.

  • AMS Subject Headings

65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1545, author = {Li , Ruo and Zhong , Wei}, title = {A Modified Adaptive Improved Mapped WENO Method}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1545--1588}, abstract = {

We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergence rates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. It produces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0057}, url = {http://global-sci.org/intro/article_detail/cicp/19940.html} }
TY - JOUR T1 - A Modified Adaptive Improved Mapped WENO Method AU - Li , Ruo AU - Zhong , Wei JO - Communications in Computational Physics VL - 5 SP - 1545 EP - 1588 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2021-0057 UR - https://global-sci.org/intro/article_detail/cicp/19940.html KW - WENO schemes, adaptive mapping functions, hyperbolic conservation laws. AB -

We propose a new family of mapped WENO schemes by using several adaptive control functions and a smoothing approximation of the signum function. The proposed schemes admit an extensive permitted range of the parameters in the mapping functions. Consequently, they have the capacity to achieve optimal convergence rates, even near critical points. Particularly, the new schemes with fine-tuned parameters illustrates a significant advantage when solving problems with discontinuities. It produces numerical solutions with high resolution without generating spurious oscillations, especially for long output times.

Li , Ruo and Zhong , Wei. (2021). A Modified Adaptive Improved Mapped WENO Method. Communications in Computational Physics. 30 (5). 1545-1588. doi:10.4208/cicp.OA-2021-0057
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