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

TL;DR

This paper introduces a sixth-order central WENO scheme with Z-type nonlinear weights for nonlinear degenerate parabolic equations, achieving high accuracy and improved resolution in smooth regions through novel reconstruction and weighting strategies.

Contribution

The paper develops a new sixth-order central WENO scheme with Z-type nonlinear weights, enhancing accuracy and stability for nonlinear degenerate parabolic equations.

Findings

Achieves sixth-order accuracy in smooth regions.

Demonstrates improved resolution in numerical examples.

Validates effectiveness through 1D and 2D tests.

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.