A static-regridding method for two-dimensional parabolic partial differential equations
Abstract: "The subject of this paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems in two space dimensions the solutions of which possess sharp moving transitions in space and time, such as steep moving f...
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
1989
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| Schriftenreihe: | Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM
1989,23 |
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| Zusammenfassung: | Abstract: "The subject of this paper belongs to the field of numerical solution of time-dependent partial differential equations. Attention is focussed on parabolic problems in two space dimensions the solutions of which possess sharp moving transitions in space and time, such as steep moving fronts and emerging and disappearing layers. For such problems, a space grid held fixed throughout the entire calculation can be computationally inefficient, since, to afford an accurate approximation, such a grid would easily have to contain a very large number of nodes. We consider a so-called static-regridding method that adapts the space grid using nested, locally uniform grids The notion of locally uniform grid refinement is an example of 'domain decomposition', the general idea of which is to decompose the original physical or computational domain into smaller subdomains and to solve the original problem on these subdomains. Hence, our computational subdomains are nested, locally uniform space grids with nonphysical boundaries which are generated up to a level of refinement good enough to resolve the anticipated fine scale structures. This way a fine grid covering the entire physical domain can be avoided. We discuss several aspects occurring in a static-regridding algorithm like ours, such as the data structure, the regridding strategy and the determination of initial and boundary conditions at course-fine grid interfaces We also present two numerical examples to demonstrate the performance of the method. The first example is hypothetical and is used to illustrate the convegence behaviour of the method. The second example originates from practice and describes a model combustion process. |
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| Beschreibung: | 27 S. |