论文标题
基于力矩的多分辨率HWENO计划双曲线保护法
Moment-based multi-resolution HWENO scheme for hyperbolic conservation laws
论文作者
论文摘要
在本文中，基于高阶的多分辨率HERMITE加权本质上是非振荡（HWENO）方案是为双曲线保护定律设计的。该方案的主要思想源自我们以前的工作[J.计算。 Phys。，446（2021）110653]，其中该函数的积分平均值及其一阶导数用于重建边界处的函数及其一阶导数值。但是，在本文中，只需要使用Zeroth和一阶矩的信息来重建一个或两个维度的高斯 - 洛巴托点的函数值。此外，还使用额外的修改程序来修改陷入困境的细胞中的一阶矩，这会改善稳定性并提高不连续性的分辨率。为了获得相同的准确性顺序，基于此力矩的多分辨率HWENO方案所需的模具大小仍然与一般的Hweno方案相同，并且比一般的WENO方案更紧凑。此外，只要它们的总和等于1，而CFL数量仍然可以为0.6，无论是一个或两个维情况，线性权重也可以是任何正数。给出了广泛的数值示例，以证明这种基于力矩的多分辨率HWENO方案的稳定性和分辨率。
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.
