This paper presents a novel inverse Lax-Wendroff (ILW) boundary treatment for finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes to solve hyperbolic conservation laws on arbitrary geometries. The complex geometric domain is divided by a uniform Cartesian grid, resulting in challenge in boundary treatment. The proposed ILW boundary treatment could provide high order approximations of both solution values and spatial derivatives at ghost points outside the computational domain. Distinct from existing ILW approaches, our boundary treatment constructs the extrapolation via optimized through a least squares formulation, coupled with the spatial derivatives at the boundary obtained via the ILW procedure. Theoretical analysis indicates that compared with other ILW methods, our proposed one would require fewer terms by using the relatively complicated ILW procedure and thus improve computational efficiency while preserving accuracy and stability. The effectiveness and robustness of the method are validated through numerical experiments.

翻译：本文提出了一种新颖的逆Lax-Wendroff边界处理方法，用于有限差分Hermite加权基本无振荡格式，以在任意几何形状上求解双曲型守恒律。复杂几何区域被均匀笛卡尔网格所划分，这给边界处理带来了挑战。所提出的逆Lax-Wendroff边界处理方法能够为计算域外部的虚拟点提供解值和空间导数的高阶近似。与现有的逆Lax-Wendroff方法不同，我们的边界处理通过最小二乘公式优化构建外推，并结合通过逆Lax-Wendroff过程获得的边界空间导数。理论分析表明，与其他逆Lax-Wendroff方法相比，我们提出的方法通过使用相对复杂的逆Lax-Wendroff过程，将需要更少的项，从而在保持精度和稳定性的同时提高计算效率。该方法的有效性和鲁棒性通过数值实验得到了验证。