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Verification of RANS solvers with manufactured solutions

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Abstract

This paper discusses code verification of Reynolds-Averaged Navier Stokes (RANS) solvers with the method of manufactured solutions (MMS). Examples of manufactured solutions (MSs) for a two-dimensional, steady, wall-bounded, incompressible, turbulent flow are presented including the specification of the turbulence quantities incorporated in several popular eddy-viscosity turbulence models. A wall-function approach for the MMS is also described. The flexiblity and usefulness of the MS is illustrated with calculations performed in three different exercises: the calculation of the flow field using the manufactured eddy-viscosity; the calculation of the eddy-viscosity using the manufactured velocity field; the calculation of the complete flow field coupling flow and turbulence variables. The results show that the numerical performance of the flow solvers is model dependent and that the solution of the complete problem may exhibit different orders of accuracy than in the exercises with no coupling between the flow and turbulence variables.

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Abbreviations

AIAA:

American Institute of Aeronautics and Astronautics

BSL:

Baseline

CFD:

Computational fluid dynamics

ERCOFTAC:

European Research Community On Flow Turbulence and Combustion

FD:

Finite-difference

FE:

Finite-elements

FV:

Finite-volume

ITTC:

International Towing Tank Conference

MS:

Manufactured solution

MMS:

Method of manufactured solutions

PDE:

Partial differential equation

RANS:

Reynolds-Averaged Navier–Stokes

SST:

Shear–Stress transport

TNT:

Turbulent/non-turbulent

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Authors and Affiliations

  1. Mechanical Engineering Department, IST, TU Lisbon, Av. Rovisco Pais 1, 1049-001, Lisbon, Portugal

    L. Eça

  2. CFD Projects, MARIN, P.O. Box 28, 6700 AA, Wageningen, The Netherlands

    M. Hoekstra

  3. Department of Mechanical Engineering, Ecole Polytechnique de Montreal, C.P. 6079, Succursalle Centre-Ville, Montreal, QC, Canada, H3C3A7

    A. Hay

  4. Department of Mechanical Engineering, Ecole Polytechnique de Montreal, C.P. 6079, Succursalle Centre-Ville, Montreal, QC, Canada, H3C3A7

    D. Pelletier

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  1. L. Eça
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  2. M. Hoekstra
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  3. A. Hay
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  4. D. Pelletier
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Correspondence to L. Eça.

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Eça, L., Hoekstra, M., Hay, A. et al. Verification of RANS solvers with manufactured solutions. Engineering with Computers 23, 253–270 (2007). https://doi.org/10.1007/s00366-007-0067-9

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