Solution of Navier–Stokes equations on a fixed mesh using conforming enrichment of velocity and pressure

Abstract

Simulation of fluid flows of multi-materials is an intriguing topic in computational mechanics. Capturing the physics of the interface between different materials poses a challenge because of the discontinuities that may occur on the interface. Several methods have been proposed in the literature to deal with this issue. In this paper, a technique based on Nitsche’s method has been employed on a fixed mesh combined with the PFEM-2 strategy for the solution of Navier–Stokes equations on multi-fluid flows. The novelty of this technique is its capability of capturing the strong and weak discontinuities and its compatibility for the application of various types of boundary conditions on the interface.

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Acknowledgements

The research that has been presented in this publication and the results obtained have been conducted and achieved with the support of the Ministerio de Economía y Competitividad (MINECO) from Spain and its funding program Ayudas para Contratos Predoctorales para la Formación de Doctores (ref. BES-2014-070613). Author Deniz C. Tanyildiz would like to express special thanks to the project: PARFLOW (ref. BIA2013-49007-C2-1-R). Dr. Riccardo Rossi would like to express special thanks to the project: EXAQUTE (ref. 800898). Moreover, the authors would like to express their gratitude to Dr. Joan Baiges from Polytechnical University of Catalonia, for his substantial help on Nitsche’s method.

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Tanyildiz, D.C., Marti, J. & Rossi, R. Solution of Navier–Stokes equations on a fixed mesh using conforming enrichment of velocity and pressure. Comp. Part. Mech. 7, 71–86 (2020). https://doi.org/10.1007/s40571-019-00285-6

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Keywords

  • Lagrangian particles
  • Multi-fluids
  • Nitsche’s method
  • Fixed mesh