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Numerical Algorithms for Divergence-Free Velocity Applications
Version 1
: Received: 15 July 2024 / Approved: 16 July 2024 / Online: 16 July 2024 (10:15:03 CEST)
How to cite: Barbi, G.; Cervone, A.; Manservisi, S. Numerical Algorithms for Divergence-Free Velocity Applications. Preprints 2024, 2024071275. https://doi.org/10.20944/preprints202407.1275.v1 Barbi, G.; Cervone, A.; Manservisi, S. Numerical Algorithms for Divergence-Free Velocity Applications. Preprints 2024, 2024071275. https://doi.org/10.20944/preprints202407.1275.v1
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
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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