AI 中文总结
该研究针对运动流体波传播产生的广义程函方程，提出基于高阶WENO的半隐式牛顿型快速扫掠方法，采用三种扫掠策略并扩展至多阶精度，经二维、三维算例验证了效率与精度。
AI 中文摘要
本文提出了基于高阶加权本质非振荡（WENO）的半隐式牛顿型高斯-赛德尔Lax-Friedrichs快速扫掠方法，用于求解运动流体中波传播问题产生的广义程函方程。该方法基于Li和Qian（2020）提出的牛顿型框架，该框架采用牛顿法沿线更新解，其雅可比矩阵为三对角且严格对角占优；在此基础上，我们通过将空间导数的高阶WENO近似引入数值哈密顿量，将局部求解器扩展至五阶、七阶和九阶精度。在高斯-赛德尔迭代框架内，考虑了列向、行向及列行交替三种扫掠策略。二维和三维空间的数值算例验证了所提格式的效率与精度。
英文摘要
In this paper, we propose high-order weighted essentially non-oscillatory (WENO)-based semi-implicit Newton-type Gauss-Seidel Lax-Friedrichs fast sweeping methods for solving the generalized Eikonal equation arising in wave propagation through a moving fluid. Building upon the Newton-type framework of Li and Qian (2020), which updates the solution line-wise using Newton's method with a tridiagonal and strictly diagonally dominant Jacobian, we extend the local solver to fifth-, seventh-, and ninth-order accuracy by incorporating high-order WENO approximations of the spatial derivatives into the numerical Hamiltonian. Three alternating sweeping strategies, namely column-wise, row-wise, and column-row-wise, are considered within the Gauss-Seidel iteration framework. Numerical examples in both two and three spatial dimensions demonstrate the efficiency and accuracy of the proposed schemes.
