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A Simple Parallel Solution Method for the Navier–Stokes Cahn–Hilliard Equations

Author

Listed:
  • Nadja Adam

    (Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany)

  • Florian Franke

    (Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany)

  • Sebastian Aland

    (Faculty of Informatics/Mathematics, HTW Dresden, Friedrich-List-Platz 1, 01069 Dresden, Germany)

Abstract

We present a discretization method of the Navier–Stokes Cahn–Hilliard equations which offers an impressing simplicity, making it easy to implement a scalable parallel code from scratch. The method is based on a special pressure projection scheme with incomplete pressure iterations. The resulting scheme admits solution by an explicit Euler method. Hence, all unknowns decouple, which enables a very simple implementation. This goes along with the opportunity of a straightforward parallelization, for example, by few lines of Open Multi-Processing (OpenMP) or Message Passing Interface (MPI) routines. Using a standard benchmark case of a rising bubble, we show that the method provides accurate results and good parallel scalability.

Suggested Citation

  • Nadja Adam & Florian Franke & Sebastian Aland, 2020. "A Simple Parallel Solution Method for the Navier–Stokes Cahn–Hilliard Equations," Mathematics, MDPI, vol. 8(8), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1224-:d:389737
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    References listed on IDEAS

    as
    1. Lee, Hyun Geun & Kim, Junseok, 2015. "An efficient numerical method for simulating multiphase flows using a diffuse interface model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 423(C), pages 33-50.
    2. Yilun Shang, 2018. "Resilient Multiscale Coordination Control against Adversarial Nodes," Energies, MDPI, vol. 11(7), pages 1-17, July.
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