A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations

TL;DR

This paper introduces a third-order semi-discrete central scheme for solving multi-dimensional hyperbolic conservation laws and convection-diffusion equations, extending previous second-order methods with high accuracy and robustness.

Contribution

It develops a new third-order semi-discrete central method that is independent of specific reconstruction techniques, enhancing accuracy and stability for complex PDEs.

Findings

Achieves high-order accuracy in numerical experiments

Demonstrates robustness across various test problems

Provides improved resolution over existing methods

Abstract

We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semi-discrete method in [16]. The method is derived independently of the specific piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results, by focusing on the new third-order CWENO reconstruction presented in [21]. The numerical results we present, show the desired accuracy, high resolution and robustness of our method.