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A simple WENO-AO method for solving hyperbolic conservation laws

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  • Huang, Cong
  • Chen, Li Li

Abstract

In this paper, we propose a simple weighted essentially non-oscillatory method with adaptive order(SWENO-AO). The SWENO-AO consists of a high order and a second-order subreconstructions with a new weight, in which the second-order subreconstruction is always smooth. Comparing to WENO-AO method developed by Zhu and Qiu (2016), the SWENO-AO has the advantage of simplicity. First, the SWENO-AO does not need to regroup the candidate cells, but uses the weighted-least-squares to obtain a smooth second-order subreconstruction directly, which is more flexible for solving multi-dimensional problem. However the WENO-AO needs to regroup the candidate cells properly for obtaining different second-order subreconstructions, so that near discontinuity, at least one of them is smooth and can be used for avoiding the spurious oscillations. Second, the SWENO-AO only consists of two subreconstructions, so the implementation is simple. However the WENO-AO uses more subreconstructions for higher dimensional problem, which increases the computational complexity. Finally, the weight of SWENO-AO is simpler than the one of WENO-AO. Numerical tests also show that, the SWENO-AO gives comparable solution as WENO-AO, but uses less computational cost, thus has higher efficiency.

Suggested Citation

  • Huang, Cong & Chen, Li Li, 2021. "A simple WENO-AO method for solving hyperbolic conservation laws," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308092
    DOI: 10.1016/j.amc.2020.125856
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    References listed on IDEAS

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    1. Feng, Hui & Huang, Cong & Wang, Rong, 2014. "An improved mapped weighted essentially non-oscillatory scheme," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 453-468.
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