TY - JOUR
T1 - A New Mapped WENO Scheme Using Order-Preserving Mapping
AU - Li , Ruo
AU - Zhong , Wei
JO - Communications in Computational Physics
VL - 2
SP - 548
EP - 592
PY - 2022
DA - 2022/01
SN - 31
DO - http://doi.org/10.4208/cicp.OA-2021-0150
UR - https://global-sci.org/intro/article_detail/cicp/20215.html
KW - Mapped WENO, order-preserving mapping, hyperbolic problems.
AB - <p style="text-align: justify;">Existing mapped WENO schemes can hardly prevent spurious oscillations
while preserving high resolutions at long output times. We reveal in this paper the essential reason of such phenomena. It is actually caused by that the mapping function
in these schemes can not preserve the order of the nonlinear weights of the stencils.
The nonlinear weights may be increased for non-smooth stencils and be decreased for
smooth stencils. It is then indicated to require the set of mapping functions to be order-preserving in mapped WENO schemes. Therefore, we propose a new mapped WENO
scheme with a set of mapping functions to be order-preserving which exhibits a remarkable advantage over the mapped WENO schemes in references. For long output
time simulations of the one-dimensional linear advection equation, the new scheme
has the capacity to attain high resolutions and avoid spurious oscillations near discontinuities meanwhile. In addition, for the two-dimensional Euler problems with strong
shock waves, the new scheme can significantly reduce the numerical oscillations.</p>