Extension of the complete flux scheme to systems of conservation laws. (English) Zbl 1259.65134
Summary: 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.
MSC:
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
Keywords:
advection-diffusion-reaction systems; flux (vector); finite volume method; integral representation of the flux; Green’s matrix; numerical flux; matrix functions; Peclet matrix; numerical examples; semidiscretizationReferences:
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