arrow
Volume 31, Issue 2
A New Mapped WENO Scheme Using Order-Preserving Mapping

Ruo Li & Wei Zhong

Commun. Comput. Phys., 31 (2022), pp. 548-592.

Published online: 2022-01

Export citation
  • Abstract

Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason of such phenomena. It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils. The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils. It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes. Therefore, we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long output time simulations of the one-dimensional linear advection equation, the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile. In addition, for the two-dimensional Euler problems with strong shock waves, the new scheme can significantly reduce the numerical oscillations.

  • AMS Subject Headings

65M06, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-31-548, author = {Li , Ruo and Zhong , Wei}, title = {A New Mapped WENO Scheme Using Order-Preserving Mapping}, journal = {Communications in Computational Physics}, year = {2022}, volume = {31}, number = {2}, pages = {548--592}, abstract = {

Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason of such phenomena. It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils. The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils. It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes. Therefore, we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long output time simulations of the one-dimensional linear advection equation, the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile. In addition, for the two-dimensional Euler problems with strong shock waves, the new scheme can significantly reduce the numerical oscillations.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2021-0150}, url = {http://global-sci.org/intro/article_detail/cicp/20215.html} }
TY - JOUR T1 - A New Mapped WENO Scheme Using Order-Preserving Mapping AU - Li , Ruo AU - Zhong , Wei JO - Communications in Computational Physics VL - 2 SP - 548 EP - 592 PY - 2022 DA - 2022/01 SN - 31 DO - http://doi.org/10.4208/cicp.OA-2021-0150 UR - https://global-sci.org/intro/article_detail/cicp/20215.html KW - Mapped WENO, order-preserving mapping, hyperbolic problems. AB -

Existing mapped WENO schemes can hardly prevent spurious oscillations while preserving high resolutions at long output times. We reveal in this paper the essential reason of such phenomena. It is actually caused by that the mapping function in these schemes can not preserve the order of the nonlinear weights of the stencils. The nonlinear weights may be increased for non-smooth stencils and be decreased for smooth stencils. It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes. Therefore, we propose a new mapped WENO scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long output time simulations of the one-dimensional linear advection equation, the new scheme has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile. In addition, for the two-dimensional Euler problems with strong shock waves, the new scheme can significantly reduce the numerical oscillations.

Ruo Li & Wei Zhong. (2022). A New Mapped WENO Scheme Using Order-Preserving Mapping. Communications in Computational Physics. 31 (2). 548-592. doi:10.4208/cicp.OA-2021-0150
Copy to clipboard
The citation has been copied to your clipboard