TY - GEN
T1 - On the accuracy of WENO schemes in the calculation of shock waves
AU - Kovyrkina, Olyana
AU - Ostapenko, Vladimir
N1 - Funding Information:
The work was carried out with support by the Russian Science Foundation (grant No. 16-11-10033).
Publisher Copyright:
© 2020 American Institute of Physics Inc.. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/24
Y1 - 2020/11/24
N2 - We have studied the integral and local accuracy of the WENO schemes in calculations with shocks propagating with a variable velocity. The integral accuracy is defined as the convergence order of spatial integrals of the difference solution calculated by the trapezoid or parabolic formulas. The local accuracy is associated with the determination of the errors in the calculation of invariants of exact solution. It is shown that when using the trapezoid formula, both the WENO3 and WENO5 schemes have only the first order of integral convergence in the intervals with one of their boundaries is in the shock influence region. If the parabolic formula is used, then the order of integral convergence for the WENO schemes decreases sharply in the intervals containing whole area of the shock wave influence. As a result, in these schemes, the local accuracy of the invariant calculations sharply decreases in the shock influence area. Moreover, in this area the local accuracy of the WENO3 and WENO5 schemes is approximately the same and much lower than the accuracy of the combined scheme, in which the Rusanov scheme is basic and the CABARET scheme is internal.
AB - We have studied the integral and local accuracy of the WENO schemes in calculations with shocks propagating with a variable velocity. The integral accuracy is defined as the convergence order of spatial integrals of the difference solution calculated by the trapezoid or parabolic formulas. The local accuracy is associated with the determination of the errors in the calculation of invariants of exact solution. It is shown that when using the trapezoid formula, both the WENO3 and WENO5 schemes have only the first order of integral convergence in the intervals with one of their boundaries is in the shock influence region. If the parabolic formula is used, then the order of integral convergence for the WENO schemes decreases sharply in the intervals containing whole area of the shock wave influence. As a result, in these schemes, the local accuracy of the invariant calculations sharply decreases in the shock influence area. Moreover, in this area the local accuracy of the WENO3 and WENO5 schemes is approximately the same and much lower than the accuracy of the combined scheme, in which the Rusanov scheme is basic and the CABARET scheme is internal.
UR - http://www.scopus.com/inward/record.url?scp=85097979876&partnerID=8YFLogxK
U2 - 10.1063/5.0026832
DO - 10.1063/5.0026832
M3 - Conference contribution
AN - SCOPUS:85097979876
T3 - AIP Conference Proceedings
BT - International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2019
A2 - Simos, Theodore E.
A2 - Tsitouras, Charalambos
PB - American Institute of Physics Inc.
T2 - International Conference on Numerical Analysis and Applied Mathematics 2019, ICNAAM 2019
Y2 - 23 September 2019 through 28 September 2019
ER -