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The Complete Flux Scheme in Cylindrical Coordinates

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Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 77))

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Abstract

We consider the complete flux (CF) scheme , a finite volume method (FVM) presented in [3]. CF is based on an integral representation for the fluxes, found by solving a local boundary value problem that includes the source term. It performs well (second order accuracy) for both diffusion and advection dominated problems. In this paper we focus on cylindrically symmetric conservation laws of advection-diffusion-reaction type.

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References

  1. Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. VII, pp. 713–1020. North-Holland, Amsterdam (2000)

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  2. Liu, L.: Studies on the discretization of plasma transport equations. Ph.D. thesis, Eindhoven University of Technology, Eindhoven (2013)

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  3. ten Thije Boonkkamp, J.H.M., anthonissen, M.J.H.: The finite volume-complete flux scheme for advection-diffusion-reaction equations. J. Sci. Comput. 46(1), 47–70 (2011)

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Correspondence to M. J. H. Anthonissen .

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Anthonissen, M.J.H., Boonkkamp, J.H.M.t.T. (2014). The Complete Flux Scheme in Cylindrical Coordinates. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_6

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