Volume 50, Issue 3
Hybrid WENO Schemes with Lax-Wendroff Type Time Discretization

Buyue Huang & Jianxian Qiu

J. Math. Study, 50 (2017), pp. 242-267.

Published online: 2017-09

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  • Abstract

In this paper, we investigate the performance of a class of the hybrid weighted essentially non-oscillatory (WENO) schemes with Lax-Wendroff time discretization procedure using different indicators for hyperbolic conservation laws. The main idea of the scheme is to use some efficient and reliable indicators to identify discontinuity of solution, then reconstruct numerical flux by WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions, hence reducing computational cost but still maintaining non-oscillatory properties for problems with strong shocks. Numerical results show that the efficiency and robustness of the hybrid WENO-LW schemes.

  • Keywords

Time discretization methods, WENO approximation, troubled-cell indicator, Hyperbolic conservation laws, Hybrid schemes.

  • AMS Subject Headings

65M60, 35L65

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

buyuehuang@qq.com (Buyue Huang)

jxqiu@xmu.edu.cn (Jianxian Qiu)

  • BibTex
  • RIS
  • TXT
@Article{JMS-50-242, author = {Buyue and Huang and buyuehuang@qq.com and 13351 and School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen 361005, Fujian, P.R. China and Buyue Huang and Jianxian and Qiu and jxqiu@xmu.edu.cn and 11019 and School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, Fujian 361005, P.R. China and Jianxian Qiu}, title = {Hybrid WENO Schemes with Lax-Wendroff Type Time Discretization}, journal = {Journal of Mathematical Study}, year = {2017}, volume = {50}, number = {3}, pages = {242--267}, abstract = {

In this paper, we investigate the performance of a class of the hybrid weighted essentially non-oscillatory (WENO) schemes with Lax-Wendroff time discretization procedure using different indicators for hyperbolic conservation laws. The main idea of the scheme is to use some efficient and reliable indicators to identify discontinuity of solution, then reconstruct numerical flux by WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions, hence reducing computational cost but still maintaining non-oscillatory properties for problems with strong shocks. Numerical results show that the efficiency and robustness of the hybrid WENO-LW schemes.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v50n3.17.03}, url = {http://global-sci.org/intro/article_detail/jms/10619.html} }
TY - JOUR T1 - Hybrid WENO Schemes with Lax-Wendroff Type Time Discretization AU - Huang , Buyue AU - Qiu , Jianxian JO - Journal of Mathematical Study VL - 3 SP - 242 EP - 267 PY - 2017 DA - 2017/09 SN - 50 DO - http://doi.org/10.4208/jms.v50n3.17.03 UR - https://global-sci.org/intro/article_detail/jms/10619.html KW - Time discretization methods, WENO approximation, troubled-cell indicator, Hyperbolic conservation laws, Hybrid schemes. AB -

In this paper, we investigate the performance of a class of the hybrid weighted essentially non-oscillatory (WENO) schemes with Lax-Wendroff time discretization procedure using different indicators for hyperbolic conservation laws. The main idea of the scheme is to use some efficient and reliable indicators to identify discontinuity of solution, then reconstruct numerical flux by WENO approximation in discontinuous regions and up-wind linear approximation in smooth regions, hence reducing computational cost but still maintaining non-oscillatory properties for problems with strong shocks. Numerical results show that the efficiency and robustness of the hybrid WENO-LW schemes.

Buyue Huang & Jianxian Qiu. (2019). Hybrid WENO Schemes with Lax-Wendroff Type Time Discretization. Journal of Mathematical Study. 50 (3). 242-267. doi:10.4208/jms.v50n3.17.03
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