TY - JOUR

T1 - Extension of the complete flux scheme to systems of conservation laws

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

AU - Dijk, van, J.

AU - Liu, L.

AU - Peerenboom, K.S.C.

PY - 2012

Y1 - 2012

N2 - We present the extension of the complete flux scheme to advection-diffusion-reaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems.
Keywords: Advection-diffusion-reaction systems · Flux (vector) · Finite volume method ·
Integral representation of the flux · Green’s matrix · Numerical flux · Matrix functions ·
Peclet matrix

AB - We present the extension of the complete flux scheme to advection-diffusion-reaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems.
Keywords: Advection-diffusion-reaction systems · Flux (vector) · Finite volume method ·
Integral representation of the flux · Green’s matrix · Numerical flux · Matrix functions ·
Peclet matrix

U2 - 10.1007/s10915-012-9588-5

DO - 10.1007/s10915-012-9588-5

M3 - Article

SN - 0885-7474

VL - 53

SP - 552

EP - 568

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

IS - 3

ER -