Efficient WENO schemes for nonuniform grids

TL;DR

This paper introduces high-order WENO schemes tailored for nonuniform grids, emphasizing their simplicity, efficiency, and accuracy, with validation through theoretical analysis and numerical experiments in conservation laws.

Contribution

The paper develops a family of high-order WENO schemes optimized for nonuniform grids, combining simplicity, efficiency, and accuracy, and demonstrates their effectiveness through analysis and experiments.

Findings

Schemes achieve high-order accuracy on nonuniform grids.

Methods are computationally efficient with linear cost relative to order.

Numerical experiments validate the schemes for conservation laws.

Abstract

A set of arbitrarily high-order WENO schemes for reconstructions on nonuniform grids is presented. These non-linear interpolation methods use simple smoothness indicators with a linear cost with respect to the order, making them easy to implement and computationally efficient. The theoretical analysis to verify the accuracy and the essentially non-oscillatory properties are presented together with some numerical experiments involving algebraic problems in order to validate them. Also, these general schemes are applied for the solution of conservation laws and hyperbolic systems in the context of finite volume methods.