Evaluating the Stability of Numerical Schemes for Fluid Solvers in Game Technology. (2nd June 2022)

• Record Type: Journal Article
• Authors: Stark, Craig R.; Diver, Declan A.
• Other Names: Zhu Peican Academic Editor.
• Is Part Of: International journal of computer games technology. Volume 2022(2022)
• Publication Date: 2022-06-02
• Subjects: Computer games -- Design -- Periodicals; Computer games -- Programming -- Periodicals; Jeux d'ordinateur; Jeux d'ordinateur -- Programmation; Computer games -- Design; Computer games -- Programming; Electronic journals; Periodicals; 794.81
• DOI: 10.1155/2022/4138315
• Languages: English
• ISSNs: 1687-7047

Abstract

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.