On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

Authors:
Roberto Bertelle;Maria Rosaria Russo;Manolo Venturin
Affiliations:
Dip. Matematica Pura ed Applicata, Università degli Studi di Padova, Padova, Italy 35121;Dip. Matematica Pura ed Applicata, Università degli Studi di Padova, Padova, Italy 35121;Dip. di Informatica, Università di Verona, Verona, Italy 37134
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2011

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Abstract

In this paper, the Minimum Polynomial Extrapolation method (MPE) is used to accelerate the convergence of the Characteristic---Based---Split (CBS) scheme for the numerical solution of steady state incompressible flows with heat transfer. The CBS scheme is a fractional step method for the solution of the Navier---Stokes equations while the MPE method is a vector extrapolation method which transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm is tested on a two-dimensional benchmark problem (buoyancy---driven convection problem) where the Navier---Stokes equations are coupled with the temperature equation. The obtained results show the feature of the extrapolation procedure to the CBS scheme and the reduction of the computational time of the simulation.