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==1 Title, abstract and keywords<!-- Your document should start with a concise and informative title. Titles are often used in information-retrieval systems. Avoid abbreviations and formulae where possible. Capitalize the first word of the title.
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==Abstract==
  
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Provide a maximum of 6 keywords, and avoiding general and plural terms and multiple concepts (avoid, for example, 'and', 'of'). Be sparing with abbreviations: only abbreviations firmly established in the field should be used. These keywords will be used for indexing purposes.
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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.
  
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An abstract is required for every document; it should succinctly summarize the reason for the work, the main findings, and the conclusions of the study. Abstract is often presented separately from the article, so it must be able to stand alone. For this reason, references and hyperlinks should be avoided. If references are essential, then cite the author(s) and year(s). Also, non-standard or uncommon abbreviations should be avoided, but if essential they must be defined at their first mention in the abstract itself. -->==
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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.
  
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The practical motivation of the work is predicting the transport of a pollutant in air in urban environments.
  
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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.
  
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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.
  
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==2 The main text<!-- You can enter and format the text of this document by selecting the ‘Edit’ option in the menu at the top of this frame or next to the title of every section of the document. This will give access to the visual editor. Alternatively, you can edit the source of this document (Wiki markup format) by selecting the ‘Edit source’ option.
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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.
  
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Most of the documents in Scipedia are written in English (write your manuscript in American or British English, but not a mixture of these). Anyhow, specific publications in other languages can be published in Scipedia. In any case, the documents published in other languages must have an abstract written in English.
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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.
  
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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.
  
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2.1 Subsections
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==Resumen==
  
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Divide your article into clearly defined and numbered sections. Subsections should be numbered 1.1, 1.2, etc. and then 1.1.1, 1.1.2, ... Use this numbering also for internal cross-referencing: do not just refer to 'the text'. Any subsection may be given a brief heading. Capitalize the first word of the headings.
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El objetivo del trabajo es desarrollar una herramienta numérica para describir cómo cambia la concentración de una o más sustancias distribuidas en un medio fluido bajo el efecto de tres procesos de transporte: advección, difusión y absorción. Para ello, es fundamental conocer la interacción de la sustancia transportada con el medio fluido.
  
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Este trabajo pretende extender métodos numéricos estabilizados para resolver las ecuaciones de transporte y flujo de fluidos de manera acoplada para una mayor precisión, eficiencia y velocidad a la hora de predecir el movimiento de las sustancias transportadas en el fluido. Se hace hincapié en el transporte de sustancias en fluidos con números de P\'eclet elevados.
  
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2.2 General guidelines
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La motivación práctica del trabajo es predecir el transporte de un contaminante en el aire en entornos urbanos.
  
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El documento resume la investigación publicada en tres artículos publicados en revistas de alto impacto del JCR en los cuales el autor del trabajo también es el primer autor. Los trabajos se adjuntan al documento en los capítulos correspondientes.
  
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La descripción de los desarrollos del trabajo se ha organizado de la siguiente manera. En primer lugar, presentamos la investigación realizada en el trabajo para el desarrollo de una formulación generalizada estabilizada de cálculo de incrementos finitos - método de elementos finitos (FIC--FEM) para resolver la ecuación transitoria multidimensional advección-difusión-absorción. El punto de partida son las ecuaciones que gobiernan los problemas multidimensionales estacionarios de advección-difusión-absorción y los problemas de advección-difusión-absorción unidimensionales transitorios obtenidos mediante el procedimiento FIC. El buen comportamiento de la nueva formulación FIC--FEM se muestra en varios ejemplos de aplicación. Este trabajo fue publicado en el primero de los tres artículos mencionados.
  
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En el siguiente capítulo presentamos un método numérico innovador para resolver problemas de transporte con altos valores de advección y / o absorción. Se ha desarrollado un enfoque lagrangiano basado en la versión actualizada del método clásico de elementos finitos de partículas (PFEM) para calcular la advección de sustancias en fluidos, mientras que se adopta una estrategia euleriana basada en la formulación estabilizada FIC--FEM para calcular los efectos de difusión y absorción. El nuevo enfoque semilagrangiano ha sido validado mediante su aplicación en una serie de ejemplos académicos de transporte de sustancias para diferentes valores de los números de P\'eclet y Damk\"ohler.
  
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Finalmente, derivamos un procedimiento para acoplar las ecuaciones de fluido y transporte para modelar la distribución de un contaminante en una calle. En nuestro caso, hemos considerado el carbono negro (BC) como contaminante. La evolución del flujo de fluido se calcula con un método estándar de elementos finitos estabilizados utilizando la técnica Quasi-Static Variational Multiscale (QS-VMS). Para la temperatura y el transporte de contaminantes utilizamos el procedimiento semilagrangiano desarrollado en el trabajo.
  
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*  Follow internationally accepted rules and conventions. In particular use the international system of units (SI). If other quantities are mentioned, give their equivalent in SI.
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Se han resuelto varios ejemplos de aplicación para ilustrar la precisión y viabilidad de la herramienta numérica propuesta para predecir el transporte de un contaminante en el aire en entornos urbanos. Uno de los ejemplos se presenta en el tercer artículo, mientras que otro académico se presenta en el apéndice de este documento.
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Latest revision as of 11:39, 15 September 2021

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.

Resumen

El objetivo del trabajo es desarrollar una herramienta numérica para describir cómo cambia la concentración de una o más sustancias distribuidas en un medio fluido bajo el efecto de tres procesos de transporte: advección, difusión y absorción. Para ello, es fundamental conocer la interacción de la sustancia transportada con el medio fluido.

Este trabajo pretende extender métodos numéricos estabilizados para resolver las ecuaciones de transporte y flujo de fluidos de manera acoplada para una mayor precisión, eficiencia y velocidad a la hora de predecir el movimiento de las sustancias transportadas en el fluido. Se hace hincapié en el transporte de sustancias en fluidos con números de P\'eclet elevados.

La motivación práctica del trabajo es predecir el transporte de un contaminante en el aire en entornos urbanos.

El documento resume la investigación publicada en tres artículos publicados en revistas de alto impacto del JCR en los cuales el autor del trabajo también es el primer autor. Los trabajos se adjuntan al documento en los capítulos correspondientes.

La descripción de los desarrollos del trabajo se ha organizado de la siguiente manera. En primer lugar, presentamos la investigación realizada en el trabajo para el desarrollo de una formulación generalizada estabilizada de cálculo de incrementos finitos - método de elementos finitos (FIC--FEM) para resolver la ecuación transitoria multidimensional advección-difusión-absorción. El punto de partida son las ecuaciones que gobiernan los problemas multidimensionales estacionarios de advección-difusión-absorción y los problemas de advección-difusión-absorción unidimensionales transitorios obtenidos mediante el procedimiento FIC. El buen comportamiento de la nueva formulación FIC--FEM se muestra en varios ejemplos de aplicación. Este trabajo fue publicado en el primero de los tres artículos mencionados.

En el siguiente capítulo presentamos un método numérico innovador para resolver problemas de transporte con altos valores de advección y / o absorción. Se ha desarrollado un enfoque lagrangiano basado en la versión actualizada del método clásico de elementos finitos de partículas (PFEM) para calcular la advección de sustancias en fluidos, mientras que se adopta una estrategia euleriana basada en la formulación estabilizada FIC--FEM para calcular los efectos de difusión y absorción. El nuevo enfoque semilagrangiano ha sido validado mediante su aplicación en una serie de ejemplos académicos de transporte de sustancias para diferentes valores de los números de P\'eclet y Damk\"ohler.

Finalmente, derivamos un procedimiento para acoplar las ecuaciones de fluido y transporte para modelar la distribución de un contaminante en una calle. En nuestro caso, hemos considerado el carbono negro (BC) como contaminante. La evolución del flujo de fluido se calcula con un método estándar de elementos finitos estabilizados utilizando la técnica Quasi-Static Variational Multiscale (QS-VMS). Para la temperatura y el transporte de contaminantes utilizamos el procedimiento semilagrangiano desarrollado en el trabajo.

Se han resuelto varios ejemplos de aplicación para ilustrar la precisión y viabilidad de la herramienta numérica propuesta para predecir el transporte de un contaminante en el aire en entornos urbanos. Uno de los ejemplos se presenta en el tercer artículo, mientras que otro académico se presenta en el apéndice de este documento.

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