Numerical Algorithms for Divergence-Free Velocity Applications

Giacomo Barbi, Antonio Cervone and Sandro Manservisi ()
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Giacomo Barbi: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Antonio Cervone: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
Sandro Manservisi: Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy

Mathematics, 2024, vol. 12, issue 16, 1-25

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.

Keywords: divergence-free velocity; Raviart–Thomas finite elements; mass conservation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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