A Lagrangian-Eulerian Finite Element algorithm for advection-diffusion-reaction problems with phase change

Author (s): Oliveira, B. ; Afonso, J. C.; Zlotnik S.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 300
Pages: 375 – 401
Date: 2015

Abstract:
This paper presents a particle-based Lagrangian-Eulerian algorithm for the solution of the unsteady advection-diffusion -reaction heat transfer equation with phase change. The algorithm combines a Lagrangian formulation for the advection + reaction problem with the Eulerian-based heat source method for the diffusion + phase change problem.
The coupling between the Lagrangian and Eulerian subproblems is achieved with a phase change detector scheme based on a local latent heat balance and a consistent/conservative interpolation technique between Lagrangian particles
and the Eulerian grid. This technique makes use of an auxiliary (finer) Eulerian grid that provides a simple and efficient method of tracking internal heterogeneities (e.g. phase boundaries), allows the use of higher order integration quadratures, and facilitates the implementation of multiscale techniques. The performance of the proposed algorithm is compared against one- and two-dimensional benchmark problems, i.e. pure rigid-body advection, isothermal and non-isothermal phase change, two-phase advective heat transfer and chemical reactions coupled with diffusion and advection. The numerical results confirm that the proposed solution method is accurate, oscillation-free and useful for and applicable to a wide range of fully coupled problems in science and engineering.

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Bibtex:

@article{Oliveira2016375,
title = "A Lagrangian–Eulerian finite element algorithm for advection–diffusion–reaction problems with phase change ",
journal = "Computer Methods in Applied Mechanics and Engineering ",
volume = "300",
number = "",
pages = "375 - 401",
year = "2016",
note = "",
issn = "0045-7825",
doi = "http://dx.doi.org/10.1016/j.cma.2015.11.028",
url = "//www.sciencedirect.com/science/article/pii/S0045782515003886",
author = "Beñat Oliveira and Juan Carlos Afonso and Sergio Zlotnik",
keywords = "Advection–diffusion–reaction",
keywords = "Phase change",
keywords = "Heat source method",
keywords = "Lagrangian–Eulerian FEM",
keywords = "Interpolation "
}