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 -