Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws

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 derived from our previous work [J. Comput. Phys., 446 (2021) 110653], in which the integral averages function and its first order derivative are used to reconstruct both values at boundaries. However, only Gauss-Lobatto points one or two dimensional case need be reconstructed by using information zeroth moments. addition, an extra modification procedure modify those moments troubled-cells, leads improvement stability enhancement resolution near discontinuities. To obtain same accuracy, size stencil required HWENO still as general more compact than WENO scheme. Moreover, linear weights can also any positive numbers long their sum equals CFL number 0.6 whether case. Extensive numerical examples given demonstrate such