A sign preserving WENO reconstruction method

TL;DR

This paper introduces SP-WENO, a third-order sign-preserving WENO reconstruction method that enhances robustness and is suitable for high-resolution entropy stable schemes for conservation laws, demonstrated through numerical experiments.

Contribution

The paper presents a novel third-order sign-preserving WENO reconstruction method with improved robustness over existing ENO schemes, applicable to multi-dimensional conservation laws.

Findings

Demonstrates the effectiveness of SP-WENO through numerical experiments.

Shows improved robustness compared to traditional ENO schemes.

Easily extendable to multi-dimensional conservation laws.

Abstract

We propose a third-order WENO reconstruction which satisfies the sign property, required for constructing high resolution entropy stable finite difference scheme for conservation laws. The reconstruction technique, which is termed as SP-WENO, is endowed with additional properties making it a more robust option compared to ENO schemes of the same order. The performance of the proposed reconstruction is demonstrated via a series of numerical experiments for linear and nonlinear scalar conservation laws. The scheme is easily extended to multi-dimensional conservation laws.