A sixth-order finite volume method for multidomain convection–diffusion problem with discontinuous coefficients

•Sixth-order finite volume method for 2D convection–diffusion problem.•Polynomial reconstructions for unstructured meshes.•Discontinuous diffusion coefficient and velocity.•Numerical experiences M-matrix preservation, positivity preservation. A sixth-order finite volume method is proposed to solve t...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 267; S. 43 - 64
Hauptverfasser: Clain, S., Machado, G.J., Nóbrega, J.M., Pereira, R.M.S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2013
Schlagworte:
Approximation
Computer simulation
Convection–diffusion
Diffusion
Diffusion coefficient
Discontinuous coefficients
Finite volume
Finite volume method
Fluxes
Heat transfer
High-order
Mathematical models
Polynomial reconstruction
Polynomials
Finite volume
Discontinuous coefficients
Convection–diffusion
High-order
Heat transfer
Polynomial reconstruction
ISSN:0045-7825, 1879-2138
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Zusammenfassung:•Sixth-order finite volume method for 2D convection–diffusion problem.•Polynomial reconstructions for unstructured meshes.•Discontinuous diffusion coefficient and velocity.•Numerical experiences M-matrix preservation, positivity preservation. A sixth-order finite volume method is proposed to solve the bidimensional linear steady-state convection–diffusion equation. A new class of polynomial reconstructions is proposed to provide accurate fluxes for the convective and the diffusive operators. The method is also designed to compute accurate approximations even with discontinuous diffusion coefficient or velocity and remains robust for large Peclet numbers. Discontinuous solutions deriving from the linear heat transfer Newton law are also considered where a decomposition domain technique is applied to maintain an effective sixth-order approximation. Numerical tests covering a large panel of situations are addressed to assess the performances of the method.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2013.08.003