Evaluating the stability of numerical schemes for fluid solvers in game technology

Stark, C. R. and Diver, D. A. (2022) Evaluating the stability of numerical schemes for fluid solvers in game technology. International Journal of Computer Games Technology, 2022, 4138315. (doi: 10.1155/2022/4138315)

Abstract

A variety of numerical techniques have been explored to solve the shallow water equations in real-time water simulations for computer graphics applications. However, determining the stability of a numerical algorithm is a complex and involved task when a coupled set of nonlinear partial differential equations need to be solved. This paper proposes a novel and simple technique to compare the relative empirical stability of finite difference (or any grid-based scheme) algorithms by solving the inviscid Burgers’ equation to analyse their respective breaking times. To exemplify the method to evaluate numerical stability, a range of finite difference schemes is considered. The technique is effective at evaluating the relative stability of the considered schemes and demonstrates that the conservative schemes have superior stability.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Diver, Professor Declan and Stark, Mr Craig
• Authors: Stark, C. R., and Diver, D. A.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: International Journal of Computer Games Technology
• Publisher: Hindawi
• ISSN: 1687-7047
• ISSN (Online): 1687-7055
• Copyright Holders: Copyright © 2022 Craig R. Stark and Declan A. Diver
• First Published: First published in International Journal of Computer Games Technology 2022: 4138315
• Publisher Policy: Reproduced under a Creative Commons License