Extension of the complete flux scheme to time-dependent conservation laws

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We present the stationary and transient complete flux schemes for the advection-diffusion-reaction equation. In the first scheme, the numerical flux is derived from a local BVP for the stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretization is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretization based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem.
Originele taal-2Engels
TitelNumerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009)
RedacteurenG. Kreiss, P. Lötstedt, A. Malqvist, M. Neytcheva
Plaats van productieBerlin
UitgeverijSpringer
Pagina's865-873
ISBN van geprinte versie978-3-642-11794-7
DOI's
StatusGepubliceerd - 2010

Vingerafdruk

dissipation
advection
test

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Thije Boonkkamp, ten, J. H. M., & Anthonissen, M. J. H. (2010). Extension of the complete flux scheme to time-dependent conservation laws. In G. Kreiss, P. Lötstedt, A. Malqvist, & M. Neytcheva (editors), Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009) (blz. 865-873). Berlin: Springer. https://doi.org/10.1007/978-3-642-11795-4 93
Thije Boonkkamp, ten, J.H.M. ; Anthonissen, M.J.H. / Extension of the complete flux scheme to time-dependent conservation laws. Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009). redacteur / G. Kreiss ; P. Lötstedt ; A. Malqvist ; M. Neytcheva. Berlin : Springer, 2010. blz. 865-873
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title = "Extension of the complete flux scheme to time-dependent conservation laws",
abstract = "We present the stationary and transient complete flux schemes for the advection-diffusion-reaction equation. In the first scheme, the numerical flux is derived from a local BVP for the stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretization is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretization based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem.",
author = "{Thije Boonkkamp, ten}, J.H.M. and M.J.H. Anthonissen",
year = "2010",
doi = "10.1007/978-3-642-11795-4 93",
language = "English",
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editor = "G. Kreiss and P. L{\"o}tstedt and A. Malqvist and M. Neytcheva",
booktitle = "Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009)",
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Thije Boonkkamp, ten, JHM & Anthonissen, MJH 2010, Extension of the complete flux scheme to time-dependent conservation laws. in G Kreiss, P Lötstedt, A Malqvist & M Neytcheva (redactie), Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009). Springer, Berlin, blz. 865-873. https://doi.org/10.1007/978-3-642-11795-4 93

Extension of the complete flux scheme to time-dependent conservation laws. / Thije Boonkkamp, ten, J.H.M.; Anthonissen, M.J.H.

Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009). redactie / G. Kreiss; P. Lötstedt; A. Malqvist; M. Neytcheva. Berlin : Springer, 2010. blz. 865-873.

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

TY - GEN

T1 - Extension of the complete flux scheme to time-dependent conservation laws

AU - Thije Boonkkamp, ten, J.H.M.

AU - Anthonissen, M.J.H.

PY - 2010

Y1 - 2010

N2 - We present the stationary and transient complete flux schemes for the advection-diffusion-reaction equation. In the first scheme, the numerical flux is derived from a local BVP for the stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretization is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretization based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem.

AB - We present the stationary and transient complete flux schemes for the advection-diffusion-reaction equation. In the first scheme, the numerical flux is derived from a local BVP for the stationary equation. The transient scheme is an extension, since it includes the time derivative in the flux computation. The resulting semidiscretization is an implicit ODE system, which has much smaller dissipation and dispersion errors than the semidiscretization based on the stationary flux, at least for smooth problems. Both schemes are validated for a test problem.

U2 - 10.1007/978-3-642-11795-4 93

DO - 10.1007/978-3-642-11795-4 93

M3 - Conference contribution

SN - 978-3-642-11794-7

SP - 865

EP - 873

BT - Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009)

A2 - Kreiss, G.

A2 - Lötstedt, P.

A2 - Malqvist, A.

A2 - Neytcheva, M.

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Thije Boonkkamp, ten JHM, Anthonissen MJH. Extension of the complete flux scheme to time-dependent conservation laws. In Kreiss G, Lötstedt P, Malqvist A, Neytcheva M, redacteurs, Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009). Berlin: Springer. 2010. blz. 865-873 https://doi.org/10.1007/978-3-642-11795-4 93