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High Level Languages Implementation and Analysis of 3D Navier-Stokes Solvers

Published online by Cambridge University Press:  03 June 2015

Valerio Grazioso ,
Carlo Scalo ,
Giuseppe de Felice  and
Carlo Meola
Valerio Grazioso*
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, 130 Stuart Street, Kingston, Ontario, Canada
Carlo Scalo*
Affiliation:
Department of Mechanical and Materials Engineering, Queen’s University, 130 Stuart Street, Kingston, Ontario, Canada
Giuseppe de Felice*
Affiliation:
Dipartimento di Energetica Termofluidodinamica applicata e Condizionamenti ambientali (DETEC), Università degli Studi di Napoli ‘Federico II’, P.le Tecchio 80, 80125 Naples, Italy
Carlo Meola*
Affiliation:
Dipartimento di Energetica Termofluidodinamica applicata e Condizionamenti ambientali (DETEC), Università degli Studi di Napoli ‘Federico II’, P.le Tecchio 80, 80125 Naples, Italy
*
Corresponding author. URL: http://me.queensu.ca/people/piomelli/research/TSMLab.php Email: [email protected]
Email: [email protected]
Email: [email protected]
Email: [email protected]
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Abstract

In this work we introduce PRIN-3D (PRoto-code for Internal flows modeled by Navier-Stokes equations in 3-Dimensions), a new high level algebraic language (Matlab®) based code, by discussing some fundamental aspects regarding its basic solving kernel and by describing the design of an innovative advection scheme. The main focus was on designing a memory and computationally efficient code that, due to the typical conciseness of the Matlab coding language, could allow for fast and effective implementation of new models or algorithms. Innovative numerical methods are discussed in the paper. The pressure equation is derived with a quasi-segregation technique leading to an iterative scheme obtained within the framework of a global preconditioning procedure. Different levels of parallelization are obtainable by exploiting special pressure variable ordering patterns that lead to a block-structured Poisson-like matrix. Moreover, the new advection scheme has the potential of a controllable artificial diffusivity. Preliminary results are shown including a fully three-dimensional internal laminar flow evolving in a relatively complex geometry and a 3D methane-air flame simulated with the aid of libraries based on the Flamelet model.

Keywords

65M1078A4876M99Matlabhigh level algebraical languagessegregationpreconditioningflamelet
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 3 , June 2011 , pp. 370 - 388
Copyright
Copyright © Global-Science Press 2011

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References

[1] Badia, S. and Codina, R., Algebraic pressure segregation methods for the incompressible naveri-stokes equations, Arch. Comput. Methods. Eng., 15 (2008), pp. 343–369.Google Scholar
[2] Ferziger, J. H. and Peric, M., Computational Methods for Fluid Dynamics, Springer-Verlag, Berlin, 2002.CrossRefGoogle Scholar
[3] George, A. and Liu, J. W., Computer Solution of Large Sparse Positive Definite Systems, Prentice-Hall, New Jersey, 1981.Google Scholar
[4] Chatzigeorgiou, A. and Stephanides, G., Evaluating performance and power of object-oriented vs. procedural programming languages, Proceedings of the 7th Ada-Europe International Conference on Reliable Software Technologies, Springer.Google Scholar
[5] Howle, V. E., Shadid, J., Elman, H. and Tuminaro, R., A parallel block multi-level pre-conditioner for the 3d incompressible Navier-Stokes equations, J. Comput. Phys., 187 (2003), pp. 504–523.Google Scholar
[6] Kim, J. and Moin, P., Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), pp. 308–323.CrossRefGoogle Scholar
[7] Erisman, A., Duff, I. and Reid, J., Direct Methods for Sparse Matrices, Oxford University Press, Oxford, 1986.Google Scholar
[8] Leveque, R. J., Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, New York, 2002.Google Scholar
[9] Meola, C. and De Felice, G., Fondamenti lineari per la Fluidodinamica Numerica, Edizioni l’Ateneo, Napoli, 1996.Google Scholar
[10] Peyret, R., Handbook of Computational Fluid Mechanics, Academic Press, London, 2000.Google Scholar
[11] Pitsch, H., Creating a flamelet library for the steady flamelet model or the flamelet/progress variable approach, User manual of: FlameMaster, A C++ Computer Program for 0D Combustion and 1D Laminar Flame Calculations, September 2006.Google Scholar
[12] Pitsch, H. and Peters, N., A consistent flamelet formulation for non-premixed combustion considering differential diffusion effects, Combust. Flames., 114 (1998), pp. 26–40.Google Scholar
[13] Morinishi, Y., Lund, T. S., Vasilyev, O. V. and Moin, P., Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys., 143 (1998), pp. 90–124.CrossRefGoogle Scholar
[14] Santoro, R. J., Puri, R. and Smyth, K. C., The oxidation of soot and carbon monoxide in hydrocarbon diffusion flames, Combust. Flames., 97 (1994), pp. 125–144.Google Scholar
[15] Rhie, C. M. and Chow, W. L., Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J., 21 (1983), pp. 1525–1532.CrossRefGoogle Scholar
[16] Ham, F. E., Lien, F. S., and Strong, A. B., A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids, J. Comput. Phys., 177 (2002), pp. 117–133.Google Scholar
[17] Grazioso, V., Massarotti, N., Meola, C. and Scalo, C., A multilevel Lagrangian conservative scheme (extended abstract), First International Conference on Computational Methods for Thermal Problems, pp. 183–186, Naples September 8-10, 2009.Google Scholar