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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| 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. |
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| ISSN: | 1687-7055 |