A novel symmetric flux limiter scheme for unstructured grids

Abstract

An appropriate flux limiter scheme and r-factor algorithm are crucial for convective discretization processes in computational fluid dynamics. To balance the accuracy, convergence, and stability of numerical simulations, a new nonlinear flux limiter scheme satisfying symmetry and smoothness is constructed based on the total variation decreasing (TVD) criterion. In addition, a new r-factor algorithm is proposed to enable implementation of TVD schemes on unstructured grids, which is achieved by employing a more reasonable reconstruction method for far upwind node position and an interpolation method requiring more upwind information. Benchmarking results for convection-dominated problems on structured and unstructured grids show that the new TVD scheme exhibits superior convergence and stability compared with classical TVD schemes, while maintaining high precision, and achieves a balance between compressibility and diffusion. Meanwhile, the new r-factor algorithm has better performance in terms of overall accuracy and convergence compared with other existing algorithms, demonstrating its potential for extensive application.