A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A two-component fluid-solid finite element model of the red blood cell

The state of the art models for the red blood cell consist of two components: A solid network of fibers (worm-like chains) that correspond to the cytoskeleton, and a fluid surface with bending stiffness that corresponds to the lipid bilayer (X. Li et.al., Phil. Trans. R. Soc. A, 372:20130389 (2014)). The fluid and solid components are connected at the junctions of the network, where trans-membrane proteins anchor the bilayer to the cytoskeleton, but this connection is not rigid and under large deformations it is possible that cytoskeleton and bilayer detach from one another. It is well know that the interactions between the lipid bilayer membrane and the skeletal network (fluid-solid interactions) are responsible for the physical properties of red blood cell. However, quantifying these interactions and studying the related dynamics is still a topic discussed and full of open questions (S. Lux, Blood, 127:187–199 (2016)). In this work we will report on our first advances towards the development of a finite element method for this strongly coupled system. It leads to a fluid-structure interaction problem, with the salient feature that both the fluid and the structure are in fact two-dimensional bodies evolving in three-dimensional space.Publicado en: Mecánica Computacional vol. XXXV, no. 9.Facultad de Ingenierí

A domain decomposition multiscale mixed method for flow in porous media based on Robin boundary conditions

In this work we propose a domain decomposition method based on Robin type boundary con- ditions that is suitable to solve the porous media equations on very large reservoirs. In order to reduce the algebraic systems to be solved to affordable sizes, a multiscale formulation is considered in which the coupling variables between subdomains, namely, pressures and normal fluxes, are seek in low dimen- sional spaces on the skeleton of the decomposition, while considering the permeability heterogeneities in the original fine grid for the local problems. In the new formulation, a non-dimensional parameter in the Robin condition is introduced such that we may transit smoothly from two well known formulations, namely, the Multiscale Mortar Mixed and the Multiscale Hybrid Mixed finite element methods. In the proposed formulation the interface spaces for pressure and fluxes can be selected independently. This has the potential to produce more accurate results by better accommodating local features of the exact solution near subdomain boundaries. Several numerical examples which exhibit highly heterogeneous permeability fields and channelized regions are solved with the new formulation and results compared to the aforementioned multiscale methods.Publicado en: Mecánica Computacional vol. XXXV, no. 17Facultad de Ingenierí

A domain decomposition multiscale mixed method for flow in porous media based on Robin boundary conditions

In this work we propose a domain decomposition method based on Robin type boundary con- ditions that is suitable to solve the porous media equations on very large reservoirs. In order to reduce the algebraic systems to be solved to affordable sizes, a multiscale formulation is considered in which the coupling variables between subdomains, namely, pressures and normal fluxes, are seek in low dimen- sional spaces on the skeleton of the decomposition, while considering the permeability heterogeneities in the original fine grid for the local problems. In the new formulation, a non-dimensional parameter in the Robin condition is introduced such that we may transit smoothly from two well known formulations, namely, the Multiscale Mortar Mixed and the Multiscale Hybrid Mixed finite element methods. In the proposed formulation the interface spaces for pressure and fluxes can be selected independently. This has the potential to produce more accurate results by better accommodating local features of the exact solution near subdomain boundaries. Several numerical examples which exhibit highly heterogeneous permeability fields and channelized regions are solved with the new formulation and results compared to the aforementioned multiscale methods.Publicado en: Mecánica Computacional vol. XXXV, no. 17Facultad de Ingenierí

A domain decomposition multiscale mixed method for flow in porous media based on Robin boundary conditions

In this work we propose a domain decomposition method based on Robin type boundary con- ditions that is suitable to solve the porous media equations on very large reservoirs. In order to reduce the algebraic systems to be solved to affordable sizes, a multiscale formulation is considered in which the coupling variables between subdomains, namely, pressures and normal fluxes, are seek in low dimen- sional spaces on the skeleton of the decomposition, while considering the permeability heterogeneities in the original fine grid for the local problems. In the new formulation, a non-dimensional parameter in the Robin condition is introduced such that we may transit smoothly from two well known formulations, namely, the Multiscale Mortar Mixed and the Multiscale Hybrid Mixed finite element methods. In the proposed formulation the interface spaces for pressure and fluxes can be selected independently. This has the potential to produce more accurate results by better accommodating local features of the exact solution near subdomain boundaries. Several numerical examples which exhibit highly heterogeneous permeability fields and channelized regions are solved with the new formulation and results compared to the aforementioned multiscale methods.Publicado en: Mecánica Computacional vol. XXXV, no. 17Facultad de Ingenierí

Simulación numérica en flujo de dos fases inmiscibles con aplicaciones en lubricación hidrodinámica

En esta tesis se discute el modelado numérico del problema de lubricación hidrodinámica en los aros de pistón de motores a explosión. Este modelado ha sido abordado con dos enfoques bien distintos. Por un lado, se ha propuesto una formulación numérica basada en el método de volúmenes finitos para resolver el modelo p–θ de Elrod–Adams, que no es otra cosa que un modelo de orden reducido para el problema de lubricación en presencia de cavitación. Por otro lado, se ha propuesto una formulación numérica completa para la simulación de flujos de dos fases inmiscibles, es decir, un modelo de mayor orden para el problema fluido–dinámico considerando la presencia por separado del lubricante y los gases. Con respecto al primer enfoque considerado, la formulación que proponemos permite resolver la ecuación de Reynolds e imponer las llamadas condiciones JFO, propuestas por Jacobson & Floberg y Olsson, resultando en una formulación estrictamente conservativa. El método está basado en un esquema de relajación y permite resolver al mismo tiempo la dinámica de las partes lubricadas. Luego de describir detalladamente el esquema, se aplica a varias situaciones prácticas y luego al problema de los aros de pistón. Si bien el método es ampliamente usado, notamos que debe ser modificado para estudiar esta clase específica de dispositivos, por lo cual proponemos una variación del mismo. La evidencia numérica en este caso parece indicar que el modelo matem ático, con esta modificación, presenta multiplicidad de soluciones, lo cual motiva el estudio del problema por medio de las ecuaciones de Navier–Stokes incompresibles. En relación con el segundo enfoque, en esta tesis se adopta una formulación de elementos finitos para las ecuaciones de Navier–Stokes, con un método de tipo level set para el seguimiento de la interfase móvil que separa las dos fases presentes en el sistema. La formulación propuesta utiliza interpolación lineal para la velocidad, presión y función de level set. Se estudian varias cuestiones particulares que deben ser tomadas en cuenta en una formulación de este tipo. Por un lado se estudia de manera exhaustiva un método de reinicialización para mantener la regularidad de la función de level set y se lo extiende al caso de mallas curvilíneas. Además, proponemos un nuevo espacio de elementos finitos, que no introduce incógnitas adicionales y está basado en simples modificaciones del espacio P_1 conforme, para capturar las discontinuidades en el campo de presiones debido a la presencia de la tensión superficial, la cual es incluida mediante una formulación de Laplace–Beltrami. La formulaciódn propuesta es monolítica, es decir, se computan simultáneamente todas las variables fluido–dinámicas (velocidad y presión) y la posición de la interfase (embebida en la función de level set), con un esquema iterativo de Newton–Raphson, para lo cual se propone un cómputo mejorado del Jacobiano. Luego, se introduce un nuevo método para acondicionar la velocidad de transporte en las cercanías de la interfase y mejorar así, en algunos casos, la precisión de los cálculos. El método está basado en la resolución de una ecuación a derivadas parciales y es por lo tanto mucho más simple de implementar que otras metodologías de tipo geométrico. Finalmente, se aplica la formulación numérica al problema fluido–dinámico en aros de pistón y los resultados son comparados con los correspondientes al modelo de lubricación propuesto

A Mass-Conserving Algorithm for Dynamical Lubrication Problems With Cavitation

A numerical algorithm for fully dynamical lubrication problems based on the Elrod-Adams formulation of the Reynolds equation with mass-conserving boundary conditions is described. A simple but effective relaxation scheme is used to update the solution maintaining the complementarity conditions on the variables that represent the pressure and fluid fraction. The equations of motion are discretized in time using Newmark`s scheme, and the dynamical variables are updated within the same relaxation process just mentioned. The good behavior of the proposed algorithm is illustrated in two examples: an oscillatory squeeze flow (for which the exact solution is available) and a dynamically loaded journal bearing. This article is accompanied by the ready-to-compile source code with the implementation of the proposed algorithm. [DOI: 10.1115/1.3142903]CNEA (Argentina)CNEA (Argentina)ANPCyT (Argentina)Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)CNPq (Brazil)FAPESP (Brazil)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CONICET (Argentina)Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina (CONICET