Preprint 2004-064

Central Runge-Kutta Schemes for Hyperbolic Conservation Laws

Lorenzo Pareschi, Gabriella Puppo and Giovanni Russo

Abstract: In this work, a new formulation for central schemes based on staggered grids is proposed. It is based on a novel approach, in which first a time discretization is carried out, followed by the space discretization. The schemes obtained in this fashion have a simpler structure than previous central schemes. For high order schemes, this simplification results in higher computational efficiency. In this work, schemes of order 2 to 5 are proposed and tested, although CRK schemes of any order of accuracy can be constructed in principle. The application to systems of equations is carefully studied, comparing algorithms based on a componentwise extension of the scalar scheme, and algorithms based on projection along characteristic directions.



Paper:
Available as PDF (840 Kbytes)
Author(s):
Lorenzo Pareschi, <pareschi@dm.unife.it>
Gabriella Puppo, <puppo@calvino.polito.it>
Giovanni Russo, <russo@dmi.unict.it>
Publishing information:
To appear in SIAM J. Sci. Comp.
Comments:
Submitted by:
<pareschi@dm.unife.it> November 25 2004.


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