TY - JOUR
T1 - Effect of Flux Evaluation Methods on the Resolution and Robustness of the Two-Step Finite-Difference WENO Scheme
AU - Kamiya , T.
AU - Asahara , M.
AU - Nonomura , T.
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 1068
EP - 1097
PY - 2020
DA - 2020/06
SN - 13
DO - http://doi.org/10.4208/nmtma.OA-2019-0033
UR - https://global-sci.org/intro/article_detail/nmtma/16967.html
KW - High-order scheme, resolution, robustness, flux evaluation, TSFDWENO scheme.
AB - <p style="text-align: justify;">The resolution and the robustness of the weighted essentially non-oscillatory (WENO) scheme and two-step finite-difference WENO (TSFDWENO) schemes
are compared by strictly using the same flux evaluation method and smoothness indicators. TSFDWENO schemes are defined to include a family of weighted compact
nonlinear scheme (WCNS) and an alternative WENO scheme. Comparison results indicate that WCNS has a higher resolution than the WENO scheme, while the WENO
scheme is more robust than WCNS. Additionally, various flux evaluation methods
are combined with TSFDWENO schemes, and they are evaluated. Then, the effects
of the flux evaluation methods on the resolution and robustness of the scheme are
investigated, and the results show that the robustness and the resolution can be significantly altered by changing the flux evaluation method. This study reveals the
advantage of being able to use various flux evaluation methods in the TSFDWENO
scheme as well as the fair comparison of the WENO schemes and WCNS. On the
other hand, these effects are marginalized when changing the interpolation and differencing method. Such knowledge can be important when selecting schemes for
actual simulation and developing guidelines for scheme improvement.</p>