This paper provides a two-dimensional fluctuation splitting scheme for unsteady hyperbolic problems which achieves third-order accuracy in both space and time. For a scalar conservation law, the sufficient conditions for a stable fluctuation splitting scheme to achieve a prescribed order of accuracy in both space and time are derived. Then, using a quadratic space approximation of the solution over each triangular element, based on the reconstruction of the gradient at the three vertices, and a four-level backward discretization of the time derivative, an implicit third-order-accurate scheme is designed. Such a scheme is extended to the Euler system and is validated versus well-known scalar-advection problems and inviscid discontinuous flows.

Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems / Rossiello, G.; DE PALMA, Pietro; Pascazio, Giuseppe; Napolitano, Michele. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 222:1(2007), pp. 332-352. [10.1016/j.jcp.2006.07.027]

Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems

DE PALMA, Pietro;PASCAZIO, Giuseppe;NAPOLITANO, Michele
2007-01-01

Abstract

This paper provides a two-dimensional fluctuation splitting scheme for unsteady hyperbolic problems which achieves third-order accuracy in both space and time. For a scalar conservation law, the sufficient conditions for a stable fluctuation splitting scheme to achieve a prescribed order of accuracy in both space and time are derived. Then, using a quadratic space approximation of the solution over each triangular element, based on the reconstruction of the gradient at the three vertices, and a four-level backward discretization of the time derivative, an implicit third-order-accurate scheme is designed. Such a scheme is extended to the Euler system and is validated versus well-known scalar-advection problems and inviscid discontinuous flows.
2007
Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems / Rossiello, G.; DE PALMA, Pietro; Pascazio, Giuseppe; Napolitano, Michele. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 222:1(2007), pp. 332-352. [10.1016/j.jcp.2006.07.027]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/2202
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