A sixth-order central WENO scheme for nonlinear degenerate parabolic equations

Abstract: In this paper we develop a new sixth-order finite difference central weighted essentially non-oscillatory (WENO) scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations. The centered polynomial is introduced for the WENO reconstruction in order to avoid the negative linear weights. We choose the Z-type nonlinear weights based on the $L^2$-norm smoothness indicators, yielding the new WENO scheme with more accurate resolution. It is also confirmed that the proposed central WENO scheme with the devised nonlinear weights achieves sixth order accuracy in smooth regions. One- and two-dimensional numerical examples are presented to demonstrate the improved performance of the proposed central WENO scheme.