Evaluating the Stability of Numerical Schemes for Fluid Solvers in Game Technology

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...

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Bibliographic Details
Main Authors: Craig R. Stark, Declan A. Diver
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:International Journal of Computer Games Technology
Online Access:http://dx.doi.org/10.1155/2022/4138315
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Summary: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.
ISSN:1687-7055