The finite volume-complete flux scheme for one-dimensional advection-diffusion-reaction equations

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We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme, which is second order accurate, uniformly in the local Peclet numbers. The flux approximation is combined with a finite volume method, and the resulting finite volume-complete flux scheme is validated for several test problems.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's16
StatusGepubliceerd - 2008

Publicatie series

NaamCASA-report
Volume0828
ISSN van geprinte versie0926-4507

Vingerafdruk

reaction-diffusion equations
advection
boundary value problems
Peclet number
finite volume method
quadratures
approximation

Citeer dit

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abstract = "We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme, which is second order accurate, uniformly in the local Peclet numbers. The flux approximation is combined with a finite volume method, and the resulting finite volume-complete flux scheme is validated for several test problems.",
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The finite volume-complete flux scheme for one-dimensional advection-diffusion-reaction equations. / Thije Boonkkamp, ten, J.H.M.; Anthonissen, M.J.H.

Eindhoven : Technische Universiteit Eindhoven, 2008. 16 blz. (CASA-report; Vol. 0828).

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AB - We present a new integral representation for the flux of the advection-diffusion-reaction equation, which is based on the solution of a local boundary value problem for the entire equation, including the source term. The flux therefore consists of two parts, corresponding to the homogeneous and particular solution of the boundary value problem. Applying suitable quadrature rules to the integral representation gives the complete flux scheme, which is second order accurate, uniformly in the local Peclet numbers. The flux approximation is combined with a finite volume method, and the resulting finite volume-complete flux scheme is validated for several test problems.

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