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DSMIE 2019: Advances in Design, Simulation and Manufacturing pp 280–288Cite as

A Semi-implicit Generalized Finite Differences Approach to Simulate Natural Convective Viscous Flows

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Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

Abstract

The purpose of this work is to carry out a Lagrangian semi-implicit Generalized Finite Differences (GFDM) implementation to simulate transient natural convective viscous flows. The solution of the incompressible Navier–Stokes equations is formulated through the first order Chorin’s projection method whilst the energy equation is implicitly discretized with the first order Euler scheme. The semi-implicit set of discretized equations is solved with the Finite Point set Method where the incorporation of the boundary conditions is done in a direct and simple manner without requiring any special treatment or stabilization. The main features behind this mesh free approach as well as details of its implementation are shown. The suitability and the accuracy of this approach for the numerical simulation of the transient natural convective viscous flows are demonstrated through the solution of the two-dimensional benchmark problem. Finally, the stability of this FPM approach is studied through the variation of parameters in the two-dimensional benchmark problem, which shows that this formulation is a promising numerical tool for the simulation of the processes involving convective thermal flows.

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Author information

Authors and Affiliations

  1. The Technological Institute of Saltillo, Blvd. V. Carranza 2400 Col. Tecnológico, 25280, Saltillo, Coahuila, Mexico

    Felix Raymundo Saucedo-Zendejo & Edgar Omar Resnediz-Flores

Authors
  1. Felix Raymundo Saucedo-Zendejo
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  2. Edgar Omar Resnediz-Flores
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Corresponding author

Correspondence to Felix Raymundo Saucedo-Zendejo .

Editor information

Editors and Affiliations

  1. Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine

    Vitalii Ivanov

  2. Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, Guangdong, China

    Yiming Rong

  3. Department of Manufacturing and Production Engineering, Poznan University of Technology, Poznan, Poland

    Justyna Trojanowska

  4. Leibniz Institute for Agricultural Engineering and Bioeconomy, Potsdam, Brandenburg, Germany

    Joachim Venus

  5. Department of Processes and Equipment of Chemical and Petroleum-Refineries, Sumy State University, Sumy, Ukraine

    Oleksandr Liaposhchenko

  6. Faculty of Manufacturing Technologies with a seat in Presov, Technical University of Kosice, Prešov, Slovakia

    Jozef Zajac

  7. Department of General Mechanics and Machine Dynamics, Sumy State University, Sumy, Ukraine

    Ivan Pavlenko

  8. Faculty of Mechanical Engineering, University of West Bohemia, Pilsen, Czech Republic

    Milan Edl

  9. Department of Information and Communication Traffic, University of Zagreb, Zagreb, Croatia

    Dragan Perakovic

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Saucedo-Zendejo, F.R., Resnediz-Flores, E.O. (2019). A Semi-implicit Generalized Finite Differences Approach to Simulate Natural Convective Viscous Flows. In: Ivanov, V., et al. Advances in Design, Simulation and Manufacturing. DSMIE 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-93587-4_29

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  • DOI: https://doi.org/10.1007/978-3-319-93587-4_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93586-7

  • Online ISBN: 978-3-319-93587-4

  • eBook Packages: EngineeringEngineering (R0)

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