Finite element methods for advection-diffusion-absorption and fluid flow problems

A. Puigferrat, E. Oñate, I. Pouplana

Finite element methods for advection-diffusion-absorption and fluid flow problems

A. Puigferrat, E. Oñate, I. Pouplana

Abstract

The objective of the work is to develop a numerical tool to describe how the concentration of one or more substances distributed in a fluid environment changes under the effect of three transport processes: advection, diffusion and absorption. For that purpose, it is essential to know the interaction of the transported substance with the fluid medium.

The work aims to develop stabilized numerical methods for solving the transport and fluid flow equations in a coupled manner for greater accuracy, efficiency and speed when predicting the motion of the transported substances in the fluid. Emphasis is put in the transport of substances in fluids at high P\'eclet numbers.

The practical motivation of the work is predicting the transport of a pollutant in air in urban environments.

The work document summarizes the research published in three papers published in JCR journals of high impact. The author of the work is also the first author in the three papers. The papers are attached to the document in the corresponding chapters.

The description of the work developments has been organized as follows. First, we present the research carried out in the work for the development of a generalized stabilized Finite Increment Calculus-Finite Element Method (FIC--FEM) formulation for solving the multidimensional transient advection-diffusion-absorption equation. The starting point of the developments are the governing equations for the multidimensional steady advection-diffusion-absorption and the unidimensional transient advection-diffusion-absorption problems obtained via the FIC procedure. The good behaviour of the new FIC--FEM formulation is shown in several examples of application. This work was published in the first of the three papers mentioned.

In the following chapter we present an innovative numerical method for solving transport problems with high values of advection and / or absorption. A Lagrangian approach based on the updated version of the classical Particle Finite Element Method (PFEM) has been developed to calculate the advection of substances in fluids, while a Eulerian strategy based on the stabilized FIC--FEM formulation is adopted to compute diffusion and absorption effects. The new semi-Lagrangian approach has been validated in its application of a series of academic examples of transport of substances for different values of the P\'eclet and Damk\"ohler numbers.

Finally, we derive a procedure for coupling the fluid and transport equations to model the distribution of a pollutant in a street canyon. In our case, we have considered black carbon (BC) as the pollutant. The evolution of the fluid flow is calculated with a standard stabilized finite element method using the Quasi-Static Variational Multiscale (QS-VMS) technique. For the temperature and pollutant transport we use the semi-Lagrangian procedure developed in the work.

Several examples of application have been solved to illustrate the accuracy and practicability of the proposed numerical tool for predicting the transport of a pollutant in air in urban environments. One of the examples are presented in the third paper, while another academic one is presented in the appendix of this document.

How to cite

A. Puigferrat, E. Oñate and I. Pouplana, Finite element methods for advection-diffusion-absorption and fluid flow problems, Monograph CIMNE (2021). M193, 114 pp. URL https://www.scipedia.com/public/Puigferrat_et_al_2021c

1 Title, abstract and keywords

2 The main text

3 Bibliography

4 Acknowledgments

5 References

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