A sixth-order weighted essentially non-oscillatory scheme for hyperbolic conservation laws

TL;DR

This paper introduces a sixth-order WENO scheme for hyperbolic conservation laws that improves accuracy by using symmetrical stencils and combines quadratic and cubic polynomials, validated through numerical tests.

Contribution

The paper proposes a novel sixth-order WENO scheme with symmetrical stencils and enhanced accuracy over classical methods within a finite volume framework.

Findings

Achieves one order of accuracy improvement over classical WENO

Demonstrates robustness and high accuracy through numerical examples

Uses a convex combination of quadratic and cubic polynomial reconstructions

Abstract

In this paper, A new sixth-order weighted essentially non-oscillatory (WENO) scheme, refered as the WENO-6, is proposed in the finite volume framework for the hyperbolic conservation laws. Instead of selecting one stencil for each cell in the classical WENO scheme [10], two independent stencils are used for two ends of the considering cell in the current approach. Meanwhile, the stencils, which are used for the reconstruction of variables at both sides of interface, are symmetrical. Compared with the classical WENO scheme [10], the current WENO scheme achieves one order of improvement in accuracy with the same stencil. The reconstruction procedure is defined by a convex combination of reconstructed values at cell interface, which are constructed from two quadratic and two cubic polynomials. The essentially non-oscillatory property is achieved by the similar weighting methodology as the classical WENO scheme. A variety of numerical examples are presented to validate the accuracy and robustness of the current scheme.