Higher Order Central Schemes for Multi-dimensional Hyperbolic Problems

TL;DR

This paper develops a fourth order central scheme for multi-dimensional hyperbolic problems using an efficient CWENO reconstruction, demonstrating high accuracy, shock capturing, and improved performance over lower-order schemes.

Contribution

It introduces a novel fourth order central scheme with optimized CWENO reconstruction for multi-dimensional hyperbolic problems, enhancing accuracy and efficiency.

Findings

Fourth order accuracy demonstrated in nonlinear problems

Scheme effectively captures shocks without oscillations

Compared to third order, it shows reduced numerical dissipation and cost

Abstract

Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and shock capturing nature of the scheme are demonstrated in various nonlinear multi-dimensional problems. In order to show the overall performance of the present central scheme numerical errors and non-oscillatory behavior are compared with existing multi-dimensional CWENO based central schemes for various multi-dimensional problems. Moreover, the benefits of the present fourth order central scheme over third order implementation are shown by comparing the numerical dissipation and computational cost between the two.