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

Onderzoeksoutput: Boek/rapportRapportAcademic

139 Downloads (Pure)

Uittreksel

We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from 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. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. Keywords. Advection-diffusion-reaction equation, flux, finite volume method, integral representation of the flux, numerical flux.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's25
StatusGepubliceerd - 2010

Publicatie series

NaamCASA-report
Volume1007
ISSN van geprinte versie0926-4507

Vingerafdruk

reaction-diffusion equations
advection
boundary value problems
finite volume method
quadratures
grids

Citeer dit

@book{ba44af3145104826825ba3070b463265,
title = "The finite volume-complete flux scheme for advection-diffusion-reaction equations",
abstract = "We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from 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. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. Keywords. Advection-diffusion-reaction equation, flux, finite volume method, integral representation of the flux, numerical flux.",
author = "{Thije Boonkkamp, ten}, J.H.M. and M.J.H. Anthonissen",
year = "2010",
language = "English",
series = "CASA-report",
publisher = "Technische Universiteit Eindhoven",

}

The finite volume-complete flux scheme for advection-diffusion-reaction equations. / Thije Boonkkamp, ten, J.H.M.; Anthonissen, M.J.H.

Eindhoven : Technische Universiteit Eindhoven, 2010. 25 blz. (CASA-report; Vol. 1007).

Onderzoeksoutput: Boek/rapportRapportAcademic

TY - BOOK

T1 - The finite volume-complete flux scheme for advection-diffusion-reaction equations

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

AU - Anthonissen, M.J.H.

PY - 2010

Y1 - 2010

N2 - We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from 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. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. Keywords. Advection-diffusion-reaction equation, flux, finite volume method, integral representation of the flux, numerical flux.

AB - We present a new finite volume scheme for the advection-diffusion-reaction equation. The scheme is second order accurate in the grid size, both for dominant diffusion and dominant advection, and has only a three-point coupling in each spatial direction. Our scheme is based on a new integral representation for the flux of the one-dimensional advection-diffusion-reaction equation, which is derived from 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. Extensions of the complete flux scheme to two-dimensional and time-dependent problems are derived, containing the cross flux term or the time derivative in the inhomogeneous flux, respectively. The resulting finite volume-complete flux scheme is validated for several test problems. Keywords. Advection-diffusion-reaction equation, flux, finite volume method, integral representation of the flux, numerical flux.

M3 - Report

T3 - CASA-report

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

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -