When using high-order schemes to solve hyperbolic conservation laws in bounded domains, it is necessary properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference treatment method proposed for Runge-Kutta methods of laws. The combines an inverse Lax-Wendroff procedure WENO type extrapolation achieve desired stability. this paper, ...

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-Loba...