A Well-Balanced Fifth-Order A-WENO Scheme Based on Flux Globalization

TL;DR

This paper introduces a new fifth-order well-balanced A-WENO scheme based on flux globalization, improving accuracy for nonconservative systems like nozzle flow and shallow water equations.

Contribution

It extends the WB path-conservative central-upwind scheme to fifth-order accuracy using flux globalization, enhancing performance for complex systems.

Findings

Demonstrates improved accuracy in numerical experiments

Effectively handles nonconservative systems

Shows advantages over previous lower-order schemes

Abstract

We construct a new fifth-order flux globalization based well-balanced (WB) alternative weighted essentially non-oscillatory (A-WENO) scheme for general nonconservative systems. The proposed scheme is a higher-order extension of the WB path-conservative central-upwind (PCCU) scheme recently proposed in [A. Kurganov, Y. Liu and R. Xin, J. Comput. Phys., 474 (2023), Paper No. 111773]. We apply the new scheme to the nozzle flow system and the two-layer shallow water equations. We conduct a series of numerical experiments, which clearly demonstrate the advantages of using the fifth-order extension of the flux globalization based WB PCCU scheme.