Fifth-Order A-WENO Finite-Difference Schemes Based on a New Adaptive Diffusion Central Numerical Flux
Baoshan Wang, Wai Sun Don, Naveen Kumar Garg, Alexander Kurganov
Abstract
A new adaptive diffusion central numerical flux within the framework of fifth-order characteristicwise alternative WENO-Z finite-difference schemes (A-WENO) with a modified local Lax--Friedrichs (LLF) flux for the Euler equations of gas dynamics is introduced. The new numerical flux adaptively adjusts the numerical diffusion coefficient present in the LLF flux. The coefficient is estimated by a suitable Rankine--Hugoniot condition, which gives a more accurate estimation of the local speed of propagation. To ensure robustness, lower and upper bounds of the coefficient are obtained with the help of the convection-pressure splitting of the Jacobian. The proposed adaptive A-WENO scheme is tested on several one- and two-dimensional benchmarks. The obtained results demonstrate that the use of the adaptive diffusion central numerical flux enhances the resolution of contact waves and improves significantly the resolution of fine-scale structures in the smooth areas of the solution while capturing shocks and high gradients in an essentially nonoscillatory manner.