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

J.H.M. Thije Boonkkamp, ten; M.J.H. Anthonissen

doi:10.1007/978-3-642-11795-4 93

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

J.H.M. Thije Boonkkamp, ten, M.J.H. Anthonissen

Scientific Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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.

Original language	English
Title of host publication	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)
Editors	G. Kreiss, P. Lötstedt, A. Malqvist, M. Neytcheva
Place of Publication	Berlin
Publisher	Springer
Pages	865-873
ISBN (Print)	978-3-642-11794-7
DOIs	https://doi.org/10.1007/978-3-642-11795-4 93
Publication status	Published - 2010

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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 (Eds.), 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) (pp. 865-873). 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). editor / G. Kreiss ; P. Lötstedt ; A. Malqvist ; M. Neytcheva. Berlin : Springer, 2010. pp. 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",

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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 (eds), 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, pp. 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). ed. / G. Kreiss; P. Lötstedt; A. Malqvist; M. Neytcheva. Berlin: Springer, 2010. p. 865-873.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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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.

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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.

PB - Springer

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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, 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). Berlin: Springer. 2010. p. 865-873 doi: 10.1007/978-3-642-11795-4 93

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

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