Novel functional weights for improving the third‐order WENO schemes.

In this article, we improved the nonlinear weight of the classical third‐order WENO scheme by using the limiter of the MUSCL scheme and got a new WENO scheme, the WENO‐F scheme, and developed three new nonlinear multiple‐parameter weight functions by improving the nonlinear weight of WENO‐JS, WENO‐Z, and WENO‐Z+ schemes. After selecting appropriate parameters of these new weight functions, three new high‐resolution schemes are comparing with three kinds of classical WENO schemes. Theoretical analysis and numerical results show that the new scheme with these multiparameter functional weights can achieve third‐order convergence in smooth regions. And the new scheme has lower dissipation and better resolution than the classical third‐order WENO schemes for smooth and discontinuous solutions. [ABSTRACT FROM AUTHOR]