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Two-dimensional (2D) hydraulic models solve the Shallow Water Equations (SWE) for the simulation of free surface flows. The necessity of considering in the calculations specific hydraulic structures, such as bridges, gates, weirs, culverts, etc., for representing more realistic flood scenarios, imply the integration in the 2D-SWE of empirical equations that represent the flow through these structures. These empirical equations are usually implemented as internal conditions over a 1D line, modifying the equations with which the flow is calculated in the edges of the mesh elements located at both sides of the line. This approach can be good enough for representing the hydraulic behavior in general. However, this 1D condition over a line, which only affects the element edges, is not a good approximation for simulating the hydrodynamics of pressurized flows, as it is the case of very wide bridges and lids over channelized rivers. New modelling strategies for simulating pressurized flows using the 2D-SWE, the Two-Component Pressure Approach method (TPA) and the Preissmann Slot Method (PSM), have been implemented in Iber. Both approaches were tested in a coverage of a channeled river characterized by several abrupt curvature changes and a contraction/expansion of their wide, and in a bridge located in a river reach that obstructs most of the floodplain. The TPA and PSM methods presented good numerical approaches for simulating pressurized flow for 2D-SWE-based models, fine-tuning the hydraulic behavior, and representing the most critical regions when a pressurized flow is generated in hydraulic structures., Postprint (published version)

[Abstract:] Numerical models based on the two-dimensional shallow water equations (2D-SWE) are routinely used in flood risk management and inundation studies. However, most of these models do not adequately account for vertically confined flow conditions that can appear during inundations, due to the presence of hydraulic structures such as bridges, culverts, or underground river reaches. In this article we propose a new mathematical modification of the standard 2D-SWE, inspired by the two-component pressure approach for 1D flows, to address the issue of transient vertically confined flows including transitions between free surface and pressurized conditions. A finite volume discretization to solve the proposed system of equations is proposed and analyzed. Various test cases are used to show the numerical stability and accuracy of the discretization, and to validate the proposed formulation. Results show that the proposed method is numerically stable, accurate, mass conservative, and preserves the C-property. It can also handle subcritical, supercritical, and transcritical flows under free surface or vertically confined conditions.

A biofilm is a layer of microorganisms attached to a surface and protected by a matrix of exopolysaccharides. Biofilm structures difficult the removal of microorganisms, thus the study of the type of structures formed throughout a biofilm life cycle is key to design elimination techniques. Also, the study of the inner mechanisms of a biofilm system is of the utmost importance in order to prevent harmful biofilms formation and enhance the properties of beneficial biofilms. This study must be achieved through the combination of mathematical modelling and experimental studies. Our work focuses on the study of biofilms formed by Listeria monocytogenes, a pathogen bacteria, specially relevant in food industry. Listeria is highly resistant to biocides and appears in common food surfaces even after decontamination processes. Their biofilms can develop quite different structures, from flat biofilms to clustered or honeycomb structures. In the present work, we develop 1D and 2D models that simulate the dynamics of biofilms formed by different strains of L. monocytogenes. All this models are solved with efficient numerical methods and robust numerical techniques, such as the Level Set method. The numerical re sults are compared with the experimental measurements obtained in the Instituto de Investigaciones Marinas, CSIC (Vigo, Spain), and the Micalis Institute, INRA (Massy, France).

[Abstract]The main goal of this PhD work is the development and numerical resolution of mathematical models that simulate the dynamics of bacterial biofilm systems, paying special attention to those biofilms formed by the Listeria monocytogenes, a pathogen of special relevance in food safety. A biofihn is a layer of microorganisms attached to a surface and protected by a matrix of exopolysaccharides. Biofilm structures difficult the removal of microorganisms, thus the study of the type of structures formed throughout a biofilm life cycle is key to design elimination techniques. In the present work, we develop different models that simulate the dynamics of biofilms formed by different strains of L. monocytogenes. We start with a 1D model that can be used to describe the formation of flat biofilms. Afterwards, we apply the acquired knowledge to develop a 2D model capable of describing more complex structures. All this models are solved with efficient numerical methods and robust numerical techniques, such as the Level Set method, that guarantees the good behaviour of the obtained solutions. Finally, the numerical results are compared with the experimental measurements obtained in the Instituto de Investigaciones Marinas, CSIC (Vigo, Spain), and the Micalis Institute, INRA (Massy, France)., [Resumen]El objetivo fundamental de esta tesis consiste en el desarrollo y resolución numérica de modelos matemáticos que reproduzcan la dinámica de biopelículas, en especial, aquellas formadas por Listeria monocytogenes, un patógeno especialmente relevante en la seguridad alimentaria. Una biopelícula es una capa de microorganismos adheridos a una superficie y protegidos por una matriz de expolisacáridos. La estructura de las biopelículas hace difícil la eliminación de los microorganismos, de ahí que sea fillldamental estudiar el tipo de estructuras que se forman durante la vida de una biopelícula para poder diseñar nuevas técnicas de eliminación. En el presente trabajo, desarrollamos modelos que simulan la dinámica de biopelículas de diferentes cepas de L. monocytogenes. Comenzamos estableciendo un modelo 1D capaz de describir la formación de biopelículas planas para, posteriormente, aplicar los conocimientos adquiridos al desarrollo de un modelo 2D capaz de describir estructuras más complejas. Estos modelos se resuelven con métodos numéricos eficientes y técnicas numéricas robustas, como el método Level Set, que garantizan el buen comportamiento de las soluciones. Finalmente, los resultados obtenidos son comparados con las imágenes de microscopía procedentes de experimentos realizados en el Instituto de Investigaciones Marinas, CSIC (Vigo, España) yen el Micalis Institute, INRA (Massy, Francia)., [Resumo ] O obxectivo fundamental desta tese é o desenvolvemento e resolución numérica de modelos matemáticos que reproduzan a dinámica de biopelículas, en especial, aquelas formadas por Lisieria monocytogenes, un patóxeno de especial relevancia na seguridade alimentaria. Unha biopelícula é unha capa de microorganismos adheridos a unha superficie e protexidos por unha matriz de expolisacáridos. A estructura das biopelículas fai difícil a eliminación dos microorganismos, de aí que sexa fundamental estudar o tipo de estructuras que se forman ao longo da vida dunha biopelícula para poder deseñar novas técnicas de eliminación. No presente traballo, desenvolvemos modelos que simulan a evolución de diferentes cepas de L. monocytogenes. Comezamos establecendo un modelo 1D capaz de describir a dinámica de cepas chás para, posteriormente, aplicar os coñecementos adquiridos ao desenvolvemento dun modelo 2D capaz de describir estruturas máis complexas. Todos estes modelos resólvense con métodos numéricos eficientes e técnicas numéricas robustas, como o método Level Set, que garanten o bo comportamento das solucións. Finalnlente, os resultados obtidos compáranse coas imáxes de microscopía obtidas en experimentos realizados no Instituto de Investigacions Mariñas, CSIC (Vigo, España) e no Micalis Institute, INRA (Massy, Francia).

The main goal of this PhD work is the development and numerical resolution of mathematical models that simulate the dynamics of bacterial biofilm systems, paying special attention to those biofilms formed by the Listeria monocytogenes, a pathogen of special relevance in food safety. A biofilm is a layer of microorganisms attached to a surface and protected by a matrix of exopolysaccharides. Biofilm structures dificult the removal of microorganisms, thus the study of the type of structures formed throughout a biofilm life cycle is key to design elimination techniques. In the present work, we develop different models that simulate the dynamics of biofilms formed by different strains of L. monocytogenes. We start with a 1D model that can be used to describe the formation of at biofilms. Afterwards, we apply the acquired knowledge to develop a 2D model capable of describing more complex structures. All this models are solved with eficient numerical methods and robust numerical techniques, such as the Level Set method, that guarantees the good behaviour of the obtained solutions. Finally, the numerical results are compared with the experimental measurements obtained in the Instituto de Investigaciones Marinas, CSIC (Vigo, Spain), and the Micalis Institute, INRA (Massy, France)

Listeria monocytogenes is a food-borne pathogen that can persist in food processing plants by forming biofilms on abiotic surfaces. The benefits that bacteria can gain from living in a biofilm, i.e., protection from environmental factors and tolerance to biocides, have been linked to the biofilm structure. Different L. monocytogenes strains build biofilms with diverse structures, and the underlying mechanisms for that diversity are not yet fully known. This work combines quantitative image analysis, cell counts, nutrient uptake data and mathematical modeling to provide a mechanistic insight into the dynamics of the structure of biofilms formed by L. monocytogenes L1A1 (serotype 1/2a) strain. Confocal laser scanning microscopy (CLSM) and quantitative image analysis were used to characterize the structure of L1A1 biofilms throughout time. L1A1 forms flat, thick structures; damaged or dead cells start appearing early in deep layers of the biofilm and rapidly and massively loss biomass after 4 days. We proposed several reaction-diffusion models to explain the system dynamics. Model candidates describe biomass and nutrients evolution including mechanisms of growth and cell spreading, nutrients diffusion and uptake and biofilm decay. Data fitting was used to estimate unknown model parameters and to choose the most appropriate candidate model. Remarkably, standard reaction-diffusion models could not describe the biofilm dynamics. The selected model reveals that biofilm aging and glucose impaired uptake play a critical role in L1A1 L. monocytogenes biofilm life cycle.

Food processes, bio-processes and bio-systems are coupled systems that may involve heat, mass and momentum transfer together with kinetic processes. This work illustrates, with a number of examples, how model-based techniques—i.e. simulation, optimization and control—offer the possibility to improve our knowledge about the system at hand and facilitate process design and optimisation even in real time. The contribution is mainly based on the authors experience and illustrates concepts with several examples such as biofilm formation, gluconic acid production, deep-fat frying of potato chips and the thermal processing of packaged foods