Semi-Lagrangian formulation for the advection–diffusion–absorption equation

We present a numerical method for solving advective–diffusive–absorptive problems with high values of advection and absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) is used to calculate advection, while a Eulerian strategy based on...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-07, Vol.380, p.113807, Article 113807
Main Authors: Puigferrat, Albert, Masó, Miguel, de-Pouplana, Ignasi, Casas, Guillermo, Oñate, Eugenio
Format: Article
Language:English
Subjects:
Absorption
Absorptivity
Advection
Convection–diffusion–reaction
Eulerian
Evolution
FIC
Finite element analysis
Finite element method
Lagrangian
Mathematical analysis
Numerical methods
PFEM
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Summary:We present a numerical method for solving advective–diffusive–absorptive problems with high values of advection and absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) is used to calculate advection, while a Eulerian strategy based on the Finite Element Method (FEM) is adopted to compute diffusion and absorption. The Eulerian FEM procedure is based on a Finite Increment Calculus (FIC) stabilized formulation recently developed by the authors. The most relevant features of each computational approach are outlined and the coupling scheme is explained. Several problems are solved to validate the method: the evolution of a localized concentration field in two dimensions (2D), the evolution of a spherical field in 3D and three benchmark problems from the literature with high absorption.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.113807