TY - JOUR
T1 - Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws
AU - Li , Jiayin
AU - Shu , Chi-Wang
AU - Qiu , Jianxian
JO - Communications in Computational Physics
VL - 2
SP - 364
EP - 400
PY - 2022
DA - 2022/08
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2022-0030
UR - https://global-sci.org/intro/article_detail/cicp/20862.html
KW - Moment-based scheme, multi-resolution scheme, HWENO scheme, hyperbolic conservation laws, KXRCF troubled-cell indicator, HLLC-flux.
AB - <p style="text-align: justify;">In this paper, a high-order moment-based multi-resolution Hermite
weighted essentially non-oscillatory (HWENO) scheme is designed for hyperbolic conservation laws. The main idea of this scheme is derived from our previous work [J.
Comput. Phys., 446 (2021) 110653], in which the integral averages of the function and
its first order derivative are used to reconstruct both the function and its first order
derivative values at the boundaries. However, in this paper, only the function values at
the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed
by using the information of the zeroth and first order moments. In addition, an extra
modification procedure is used to modify those first order moments in the troubled-cells, which leads to an improvement of stability and an enhancement of resolution
near discontinuities. To obtain the same order of accuracy, the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the
general HWENO scheme and is more compact than the general WENO scheme. Moreover, the linear weights are not unique and are independent of the node position, and
the CFL number can still be 0.6 whether for the one or two dimensional case, which has
to be 0.2 in the two dimensional case for other HWENO schemes. Extensive numerical
examples are given to demonstrate the stability and resolution of such moment-based
multi-resolution HWENO scheme.</p>