Iterative Implementation of an Implicit–Explicit Hybrid Scheme for Hydrodynamics

✍ Scribed by Wenlong Dai; Paul R. Woodward

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 446 KB
• Volume: 124
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0054

✦ Synopsis

are favored over their explicit counterparts for some problems, in which the time-step size necessary for procuring Iterative implementation of an implicit-explicit hybrid scheme for solving the Euler equations is described in this paper. The a required temporal accuracy may be significantly larger scheme was proposed by Fryxell et al. (J. Comput. Phys. 63, 283 than that dictated by the explicit stability condition. Im-(1986)), is of the Godunov-type in both explicit and implicit regimes, plicit-explicit hybrid schemes are useful when a flow atis conservative, and is accurate to second order in both space and tains different wave speeds either in different regions or time for all Courant numbers. Only a single level of iterations is at different instants, and the time accuracy is important in involved in the implementation, which solves both the implicit relations arising from upstream centered differences for all wave famisome parts of simulation domains.

lies and the nonlinearity of the Euler equations. The number of Implicit and implicit-explicit hybrid schemes for hydroiterations required to reach a converged solution may be signifidynamical equations have been developed for many years.

cantly reduced by the introduction of the multicolors proposed in Schemes with a smooth switch for advection have been in this paper. Only a small number of iterations are needed in the scheme for a simulation with large time steps. The multicolors may use for many years (for example, see [8, 9]). Beam and also be applied to other linear and nonlinear wave equations for Warming [10] proposed an implicit scheme for hyperbolic numerical solutions.