Affiliation:
1. Laboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, Italy
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.
Reference44 articles.
1. Raviart, P.A., and Thomas, J.M. (1983). Introduction à l’Analyse Numérique des Équations aux Dérivées Partielles, Masson.
2. On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime;Linke;Comput. Methods Appl. Mech. Eng.,2014
3. Girault, V., and Raviart, P.A. (1986). Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms, Springer.
4. Fortin, M., and Brezzi, F. (1991). Mixed and Hybrid Finite Element Methods, Springer.
5. Elman, H., Silvester, D., and Wathen, A. (2014). Finite Elements and Fast Iterative Solvers: With Applications in Incompressible Fluid Dynamics, Oxford University Press.