Naslov
Efficient implementation of WENO schemes to nonuniform meshes

Autori
Črnjarić-Žic, Nelida ; Maćešić, Senka ; Crnković, Bojan

Izvornik
Annali dell'Università di Ferrara. Sezione 7: Scienze matematiche (0430-3202) 53 (2007); 199-215

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
nonuniform mesh; finite volume WENO schemes; hyperbolic balance

Sažetak
Most of the standard papers about the WENO schemes consider their implementation to uniform meshes only. In that case the WENO reconstruction is preformed efficiently by using the algebraic expressions for evaluating the reconstruction values and the smoothness indicators from cell averages. The coefficients appearing in these expressions are constant, dependent just on the scheme order, not on the mesh size or the reconstruction function values, and can be found, for example, in Jiang, Shu, Efficient implementation of WENO schemes, J. Comp. Physics, 1996. In problems where the geometrical properties must be taken into account or the solution has localized fine scale structure that must be resolved, it is computationally efficient to do local grid refinement, and therefore also desirable to have numerical schemes, which can be applied to nonuniform meshes. Finite volume WENO schemes extend naturally to nonuniform meshes although the reconstruction becomes quite complicated, depending on the complexity of the grid structure. In this paper we propose an efficient implementation of finite volume WENO schemes to nonuniform meshes. In order to save the computational cost in the nonuniform case, we suggest the way for precomputing the coefficients and linear weights for different orders of WENO schemes. Furthermore, for the smoothness indicators that are defined in an integral form we present the corresponding algebraic expressions in which the coefficients obtained as a linear combination of divided differences arise. In order to validate the new implementation, resulting schemes are applied in different test examples.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

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