2025/11/27 by Liang Li, Li, Liang, Jun Zhu +5
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2511.22790
openalex publication_date 2025/11/27 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-order hybrid fast sweeping scheme for solving steady state problems of hyperbolic conservation laws. Unlike many other fast sweeping methods, the explicit property of fixed-point fast sweeping methods provides flexibility to apply the alternative weighted essentially non-oscillatory (AWENO) scheme with unequal-sized substencils as the local solver, which facilitates the usage of arbitrary monotone numerical fluxes. Furthermore, a novel hybrid technique is designed in the local solver to combine the nonlinear AWENO interpolation with the linear scheme for an additional improvement in efficiency of the high-order fast sweeping iterations. Numerical examples show that the developed fixed-point fast sweeping hybrid AWENO method with unequal-sized substencils can achieve absolute convergence (i.e., the residue of the fast sweeping iterations converges to machine zero / round off errors) more easily than the original AWENO method with equal-sized substencils, and is more efficient than the popular third-order total variation diminishing (TVD) Runge-Kutta time-marching approach to converge to steady state solutions.