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SUMMARY:Complete flux schemes for conservation laws of advection-diffusion
-reaction type
DTSTART;VALUE=DATE-TIME:20160617T092500Z
DTEND;VALUE=DATE-TIME:20160617T101000Z
DTSTAMP;VALUE=DATE-TIME:20190819T205932Z
UID:indico-contribution-2968@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jan ten Thije Boonkkamp (Department of Mathematics a
nd Computer Science)\nComplete flux schemes are recently developed numeric
al flux approximation schemes for conservation laws of advection-diffusion
-reaction type\; see e.g. [1\, 2]. The basic complete flux scheme is deriv
ed from a local one-dimensional boundary value problem for the entire equa
tion\, including the source term. Consequently\, the integral representati
on of the flux contains a homogeneous and an inhomogeneous part\, correspo
nding to the advection-diffusion operator and the source term\, respective
ly. Suitable quadrature rules give the numerical flux.\n\nFor time-depende
nt problems\, the time derivative is considered a source term and is inclu
ded in the inhomogeneous flux\, resulting in an implicit semi-discretisati
on. The implicit system proves to have much smaller dissipation and disper
sion errors than the standard semidiscrete system\, especially for dominan
t advection.\n\nJust as for scalar equations\, for coupled systems of cons
ervation laws\, the complete flux approximation is derived from a local sy
stem boundary value problem\, this way incorporatin the coupling between t
he constituent equations in the discretization. Also in the system case\,
the numerical flux (vector) is the superpostion of a homogeneous and an in
homogeneous component\, corresponding to the advection-diffusion operator
and the source term vector\, respectively. The scheme is applied to multi-
species diffusion and satisfies the mass constraint exactly.\n\n\n\nRefere
nces\n\n[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen\, The finite
volume-complete flux scheme for advection-diffusion-reaction equations\,
J. Sci. Comput. 46\, pp. 47-70 (2011).\n\n[2] J.H.M. ten Thije Boonkkamp\,
J. van Dijk\, L. Liu and K.S.C. Peerenboom\, Extension of the complete fl
ux scheme to systems of comservation laws\, J. Sci. Comput. 53\, pp. 552-5
68 (2012).\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2968/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2968/
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