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Erschienen in:
2016 | OriginalPaper | Buchkapitel
Complete Flux Scheme for Conservation Laws Containing a Linear Source
verfasst von : J. H. M. ten Thije Boonkkamp, B. V. Rathish Kumar, S. Kumar, M. Pargaei
Erschienen in: Numerical Mathematics and Advanced Applications ENUMATH 2015
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Abstract
We present an extension of the complete flux scheme for conservation laws containing a linear source. In our new scheme, we split off the linear part of the source and incorporate this term in the homogeneous flux, the remaining nonlinear part is included in the inhomogeneous flux. This approach gives rise to modified homogeneous and inhomogeneous fluxes, which reduce to the classical fluxes for vanishing linear source. On the other hand, if the linear source is large, the solution of the underlying boundary value problem is oscillatory, resulting in completely different numerical fluxes. We demonstrate the performance of the homogeneous flux approximation.