The NIRVANA scheme applied to one-dimensional advection. (English) Zbl 0849.76063
The NIRVANA project which is an ongoing quest of an explicit, single-time-step, conservative, flux-based, highly accurate, nonoscillatory finite-volume CFD scheme for multidimensional advection-dominated flows, without restriction on the time-step, has been taken up, and some of the features have been demonstrated by carrying out an analysis for the simplest situation (pure one-dimensional avection at constant velocity on a uniform grid). Finally, from the viewpoint of applied CFD, the paper outlines possible avenues for generalization aimed at the development of practical algorithms for highly advective, nonlinear, multidimensional flows. This makes the study of this paper as of permanent interest.
Reviewer: V.P.Tyagi (Bombay)
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
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