On stabilized integration for time-dependent PDEs
An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly. The method is a special two-step form of the one-step IMEX (implicit–explicit) RKC (Runge–Kutta–Chebyshev) method. The special two-step form is introduce...
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| Veröffentlicht in: | Journal of computational physics 2007-05, Vol.224 (1), p.3-16 |
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| container_title | Journal of computational physics |
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| creator | Sommeijer, B.P. Verwer, J.G. |
| description | An integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly. The method is a special two-step form of the one-step IMEX (implicit–explicit) RKC (Runge–Kutta–Chebyshev) method. The special two-step form is introduced with the aim of getting a non-zero imaginary stability boundary which is zero for the one-step method. Having a non-zero imaginary stability boundary allows, for example, the integration of pure advection equations space-discretized with centered schemes, the integration of damped or viscous wave equations, the integration of coupled sound and heat flow equations, etc. For our class of methods it also simplifies the choice of temporal step sizes satisfying the von Neumann stability criterion, by embedding a thin long rectangle inside the stability region. Embedding rectangles or other tractable domains with this purpose is an idea of Wesseling. |
| doi_str_mv | 10.1016/j.jcp.2006.11.013 |
| format | Article |
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| subjects | Computational techniques Coupled sound and heat flow Damped wave equations Exact sciences and technology Mathematical methods in physics Numerical integration Physics Reactive flow problems Runge–Kutta–Chebyshev methods Stabilized explicit integration |
| title | On stabilized integration for time-dependent PDEs |
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