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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
