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

Craig R. Stark*, Declan A. Diver

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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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.
Original languageEnglish
Article number4138315
Pages (from-to)1-11
Number of pages11
JournalInternational Journal of Computer Games Technology
Volume2022
Early online date2 Jun 2022
DOIs
Publication statusPublished - 2 Jun 2022

Keywords

  • Computational fluid dynamics
  • Numerical stability
  • Numerical schemes
  • Finite difference method
  • Computer games
  • Technology
  • Physics engine

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