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Numerical Algorithms for Divergence-Free Velocity Applications

Author

Listed:
  • Giacomo Barbi

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Antonio Cervone

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

  • Sandro Manservisi

    (Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
    These authors contributed equally to this work.)

Abstract

This work focuses on the well-known issue of mass conservation in the context of the finite element technique for computational fluid dynamic simulations. Specifically, non-conventional finite element families for solving Navier–Stokes equations are investigated to address the mathematical constraint of incompressible flows. Raviart–Thomas finite elements are employed for the achievement of a discrete free-divergence velocity. In particular, the proposed algorithm projects the velocity field into the discrete free-divergence space by using the lowest-order Raviart–Thomas element. This decomposition is applied in the context of the projection method, a numerical algorithm employed for solving Navier–Stokes equations. Numerical examples validate the approach’s effectiveness, considering different types of computational grids. Additionally, the presented paper considers an interface advection problem using marker approximation in the context of multiphase flow simulations. Numerical tests, equipped with an analytical velocity field for the surface advection, are presented to compare exact and non-exact divergence-free velocity interpolation.

Suggested Citation

  • Giacomo Barbi & Antonio Cervone & Sandro Manservisi, 2024. "Numerical Algorithms for Divergence-Free Velocity Applications," Mathematics, MDPI, vol. 12(16), pages 1-25, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:16:p:2514-:d:1456474
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