The discontinuous control-volume/finite-element method is applied to the one-dimensional advection-diffusion equation. The aforementioned methodology is relatively novel and has been mainly applied for the solution of pure-advection problems. This work focuses on the main features of an accurate representation of the diffusion operator, which are investigated both by Fourier analysis and numerical experiments. A mixed formulation is followed, where the constitutive equation for the diffusive flux is not substituted into the conservation equation for the transported scalar. The Fourier analysis of a linear, diffusion problem shows that the resolution error is both dispersive and dissipative, in contrast with the purely dissipative error of the traditional continuous Galerkin approximation.

Discontinuous control-volume/finite-element method for advection-diffusion problems

STIPCICH, GORAN;PILLER, MARZIO;PIVETTA, MARCO;ZOVATTO, LUIGINO
2011

Abstract

The discontinuous control-volume/finite-element method is applied to the one-dimensional advection-diffusion equation. The aforementioned methodology is relatively novel and has been mainly applied for the solution of pure-advection problems. This work focuses on the main features of an accurate representation of the diffusion operator, which are investigated both by Fourier analysis and numerical experiments. A mixed formulation is followed, where the constitutive equation for the diffusive flux is not substituted into the conservation equation for the transported scalar. The Fourier analysis of a linear, diffusion problem shows that the resolution error is both dispersive and dissipative, in contrast with the purely dissipative error of the traditional continuous Galerkin approximation.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2367780
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