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 can also be any positive numbers as long as their sum equals one and the CFL number can still be 0.6 whether for the one or two dimensional case. Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.
翻译:在本文中,为双曲线保护法设计了一个基于高阶瞬时的多分解赫米特(HWENO)加权基本非悬浮性多分解(HWENO)方案,其主要想法来自我们以前的工作[J.Compuut.Phys.,446 (2021)110653],其中函数及其第一级衍生物的综合平均值用于在边界重建函数及其第一级衍生值。然而,在本文件中,只有高斯-洛巴托点在一或二维情况下的函数值需要利用零点和第一顺序时间的信息来重建。此外,还使用了额外的修改程序来修改混乱细胞中的第一顺序时间,从而导致稳定性的改善和分辨率接近不连续性的增强。为了获得同样的准确性,这一基于时间的多分辨率HWENO方案所需的极小的大小与一般HWENO方案相同,比一般WENO方案更为紧凑。此外,线性加权权重也可能是目前给出的任何硬性数字数字,作为给WENO方案的两个分辨率和数字。