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A pseudo-DNS method for the simulation of incompressible fluid flows with instabilities at different scales

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Abstract

In this work, a new model for the analysis of incompressible fluid flows with massive instabilities at different scales is presented. It relies on resolving all the instabilities at all scales without any additional model, i.e., following the direct numerical simulation style. Nevertheless, the computation is carried out at two levels or scales, termed the coarse and the fine. The fine-scale simulation is performed on representative volume elements providing the homogenized stress tensor as a function of several dimensionless numbers characterizing the flow. Consequently, the effect of the fine-scale instabilities is transferred to the coarse level as a homogenized stress tensor, a procedure inspired by standard multi-scale methods used in solids. The present proposal introduces a new way for the treatment of the flow at the fine scale, simulating not only the coarse scale but also the fine scale with all the necessary detail, but without incurring in the excessive computational cost of the classical DNS. Another interesting aspect of the present proposal is the use of a Lagrangian formulation for convecting the eddies simulated on the fine mesh through the coarse domain. Several examples showing the potentiality of this methodology for the simulation of homogeneous flows are presented.

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Acknowledgements

The authors express their most sincere gratitude to Xavier Oliver, Alfredo Huespe, and Pablo Sanchez for many fruitful discussions and valuable advises regarding the multi-scale methods. We sincerely thank Eugenio Oñate for continuous support and multiple suggestions for alleviating the problems faced in the development of the method. We also thank Pablo Becker for his trials which allowed us to obtain first unstable solutions on an RVE. Axel Larreteguy wishes to acknowledge the support from UADE and Banco Santander RIO through Grant BSR181. Juan Gimenez and Norberto Nigro wish to acknowledge CONICET, Universidad Nacional del Litoral (CAI+D 2016 PJ 50020150100018LI), and Agencia Nacional de Promoción Científica y Tecnológica (PICT 2016-2908).

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Authors and Affiliations

  1. International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain

    Sergio Idelsohn & Pavel Ryzhakov

  2. Centro de Investigación de Métodos Computacionales (CIMEC), Santa Fe, Argentina

    Sergio Idelsohn, Norberto Nigro & Juan M. Gimenez

  3. Universidad Argentina de la Empresa (UADE), Buenos Aires, Argentina

    Axel Larreteguy

Authors
  1. Sergio Idelsohn
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  2. Norberto Nigro
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  3. Axel Larreteguy
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  4. Juan M. Gimenez
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Correspondence to Sergio Idelsohn.

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Idelsohn, S., Nigro, N., Larreteguy, A. et al. A pseudo-DNS method for the simulation of incompressible fluid flows with instabilities at different scales. Comp. Part. Mech. 7, 19–40 (2020). https://doi.org/10.1007/s40571-019-00264-x

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