Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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AN IMPROVED ALTERNATIVE WENO SCHEMES WITH PERTURBATIONAL TERMS FOR THE HYPERBOLIC CONSERVATION LAWS

  • KUNMIN SUNG (DEPARTMENT OF MATHEMATICAL SCIENCES AND RESEARCH INSTITUTE OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY) ;
  • YOUNGSOO HA (DEPARTMENT OF MATHEMATICAL SCIENCES AND RESEARCH INSTITUTE OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY) ;
  • MYUNGJOO KANG (DEPARTMENT OF MATHEMATICAL SCIENCES AND RESEARCH INSTITUTE OF MATHEMATICS, SEOUL NATIONAL UNIVERSITY)
  • Received : 2023.10.11
  • Accepted : 2023.11.17
  • Published : 2023.12.25
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Abstract

This paper aims to improve the alternative formulation of the fifth- and sixth-order accurate weighted essentially non-oscillatory (AWENO) finite difference schemes. The first is to derive the AWENO scheme with sixth-order accuracy in the smooth region of the solution. Second, a new weighted polynomial functions combining the perturbed forms with conserved variable to the AWENO is constructed; the new form of tunable functions are invented to maintain non-oscillatory property. Detailed numerical experiments are presented to illustrate the behavior of the new perturbational AWENO schemes. The performance of the present scheme is evaluated in terms of accuracy and resolution of discontinuities using a variety of one and two-dimensional test cases. We show that the resulted perturbational AWENO schemes can achieve fifth- and sixth-order accuracy in smooth regions while reducing numerical dissipation significantly near singularities.

Keywords

Acknowledgement

This work was supported by the Challengeable Future Defense Technology Research and Development Program through the Agency for Defense Development(ADD) funded by the Defense Acquisition Program Administration in 2021(No. 915020201). Also, this work was supported by the grant of NRF-2021R1A2C1095443 and ICT R&D program of MOTIE (P0014715).

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