Improved third‐order weighted essentially nonoscillatory schemes with new smoothness indicators

Abstract

In this article, we present two improved third-order weighted essentially nonoscillatory (WENO) schemes for recovering their design-order near first-order critical points. The schemes are constructed in the framework of third-order WENO-Z scheme. Two new global smoothness indicators, τ L3 and τ L4 , are devised by a nonlinear combination of local smoothness indicators (IS k) and reference values (IS G) based on Lagrangian interpolation polynomial. The performances of the proposed schemes are evaluated on several numerical tests governed by one-dimensional linear advection equation or oneand two-dimensional Euler equations. Numerical results indicate that the presented schemes provide less dissipation and higher resolution than the original WENO3-JS and subsequent WENO3-N scheme.

A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations

“…In addition, many other scholars have improved the third-order WENO scheme and developed many new schemes. [42,43,44] However, the various current third-order WENO schemes suffer from two shortcomings: First, they cannot achieve optimal accuracy at high-order critical points. Second, some high-resolution WENO schemes suffer from relatively complicated construction of the weight function and low computational efficiency.…”