TY - JOUR
T1 - Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes
AU - Wang, BaoShan
AU - Don, Wai Sun
AU - Kurganov, Alexander
AU - Liu, Yongle
N1 - The work of B. S. Wang and W. S. Don was partially supported by the Ocean University of China through grant 201712011. The work of A. Kurganov was supported in part by NSFC grants 11771201 and 1201101343 and by the fund of the Guangdong Provincial Key Laboratory of Computational Science and Material Design (No. 2019B030301001).
Publisher Copyright:
© 2021, Shanghai University.
PY - 2023/3
Y1 - 2023/3
N2 - We construct new fifth-order alternative WENO (A-WENO) schemes for the Euler equations of gas dynamics. The new scheme is based on a new adaptive diffusion central-upwind Rankine-Hugoniot (CURH) numerical flux. The CURH numerical fluxes have been recently proposed in [Garg et al. J Comput Phys 428, 2021] in the context of second-order semi-discrete finite-volume methods. The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux, which was also developed with the help of the discrete Rankine-Hugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in [Wang et al. SIAM J Sci Comput 42, 2020]. As in that work, we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes. The resulting one- and two-dimensional schemes are tested on a number of numerical examples, which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.
AB - We construct new fifth-order alternative WENO (A-WENO) schemes for the Euler equations of gas dynamics. The new scheme is based on a new adaptive diffusion central-upwind Rankine-Hugoniot (CURH) numerical flux. The CURH numerical fluxes have been recently proposed in [Garg et al. J Comput Phys 428, 2021] in the context of second-order semi-discrete finite-volume methods. The proposed adaptive diffusion CURH flux contains a smaller amount of numerical dissipation compared with the adaptive diffusion central numerical flux, which was also developed with the help of the discrete Rankine-Hugoniot conditions and used in the fifth-order A-WENO scheme recently introduced in [Wang et al. SIAM J Sci Comput 42, 2020]. As in that work, we here use the fifth-order characteristic-wise WENO-Z interpolations to evaluate the fifth-order point values required by the numerical fluxes. The resulting one- and two-dimensional schemes are tested on a number of numerical examples, which clearly demonstrate that the new schemes outperform the existing fifth-order A-WENO schemes without compromising the robustness.
KW - A-WENO schemes
KW - Central-upwind schemes
KW - Discrete Rankine-Hugoniot conditions
KW - Euler equations of gas dynamics
KW - Local speeds of propagation
KW - Numerical dissipation switch
UR - http://www.scopus.com/inward/record.url?scp=85132435631&partnerID=8YFLogxK
U2 - 10.1007/s42967-021-00161-2
DO - 10.1007/s42967-021-00161-2
M3 - Journal article
AN - SCOPUS:85132435631
SN - 2096-6385
VL - 5
SP - 295
EP - 314
JO - Communications on Applied Mathematics and Computation
JF - Communications on Applied Mathematics and Computation
IS - 1
ER -