Development of a mixed control volume – Finite element method for the advection–diffusion equation with spectral convergence |
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Authors: | M. Piller E. Stalio |
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Affiliation: | aUniversità degli Studi di Trieste, Dipartimento di Ingegneria Civile e Ambientale, Sezione Georisorse e Ambiente, via A. Valerio 10, 34127 Trieste, Italy;bUniversità degli Studi di Modena e Reggio Emilia, Dipartimento di Ingegneria Meccanica e Civile, via Vignolese 905/B, 41125 Modena, Italy |
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Abstract: | In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining high-orders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection–diffusion equation. The numerical method and its implementation are carefully tested in the paper where h- and p-convergence are checked by comparing numerical results against analytical solutions in several relevant test-cases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill-conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and control-volume edges. |
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Keywords: | Advection&ndash diffusion equation Matrix conditioning hp-Convergence Quadrature free method CVFEM |
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