Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws (Communications in Computational Physics, 2022)
In this paper, a high-order moment-based multi-resolution Hermiteweighted 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 andits first order derivative are used to reconstruct both the function and its first orderderivative values at the boundaries. However, in this paper, only the function values atthe Gauss-Lobatto points in the one or two dimensional case need to be reconstructedby using the information of the zeroth and first order moments. In addition, an extramodification procedure is used to modify those first order moments in the troubled-cells, which leads to an improvement of stability and an enhancement of resolutionnear 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 thegeneral 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, andthe CFL number can still be 0.6 whether for the one or two dimensional case, which hasto be 0.2 in the two dimensional case for other HWENO schemes. Extensive numericalexamples are given to demonstrate the stability and resolution of such moment-basedmulti-resolution HWENO scheme.