三阶WENO-Z格式精度分析及其改进格式

Abstract

Firstly, the sufficient conditions for the 3rd-order WENO scheme satisfying the convergence precision were deduced. Based on the Taylor series method, the precision of the conventional 3rd-order WENO-Z scheme in the smooth flow field was analyzed. It was found that at the critical points, the 3rd-order WENO-Z scheme fails to achieve the convergence precision. In order to improve the precision near the critical points for the 3rd-order WENO-Z scheme, an improved 3rd-order WENO-Z scheme (WENO-NZ3) was constructed in view of the balance between precision and stability to finally determine the parameters. The improvement of the precision was verified through 2 typical numerical tests. What is more, the Sod shock wave tube, the shock-entropy wave interaction, the Rayleigh-Taylor instability and the 2D Riemann problem were calculated to confirm that the WENO-NZ3 scheme performs better than the conventional WENO schemes like WENO-JS3, WENO-Z3 and WENO-N3.