ISSN:
0961-5539
Source:
Emerald Fulltext Archive Database 1994-2005
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Purpose - An original finite element scheme for advection-diffusion-reaction problems is presented. The new method, called spotted Petrov-Galerkin (SPG), is a quadratic Petrov-Galerkin (PG) formulation developed for the solution of equations where either reaction (associated to zero-order derivatives of the unknown) and/or advection (proportional to first-order derivatives) dominates on diffusion (associated to second-order derivatives). The addressed issues are turbulence and advective-reactive features in modelling turbomachinery flows. Design/methodology/approach - The present work addresses the definition of a new PG stabilization scheme for the reactive flow limit, formulated on a quadratic finite element space of approximation. We advocate the use of a higher order stabilized formulation that guarantees the best compromise between solution stability and accuracy. The formulation is first presented for linear scalar one-dimensional advective-diffusive-reactive problems and then extended to quadrangular Q2 elements. Findings - The proposed advective-diffusive-reactive PG formulation improves the solution accuracy with respect to a standard streamline driven stabilization schemes, e.g. the streamline upwind or Galerkin, in that it properly accounts for the boundary layer region flow phenomena in presence of non-equilibrium effects. Research limitations/implications - The numerical method here proposed has been designed for second-order quadrangular finite-elements. In particular, the Reynolds-Averaged Navier-Stokes equations with a non-linear turbulence closure have been modelled using the stable mixed element pair Q2-Q1. Originality/value - This paper investigated the predicting capabilities of a finite element method stabilized formulation developed for the purpose of solving advection-reaction-diffusion problems. The new method, called SPG, demonstrates its suitability in solving the typical equations of turbulence eddy viscosity models.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1108/09615530510625147
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