Developing numerical methods for fully-coupled nonlinear fluid-structure interaction problems

This thesis is dedicated to developing numerical methods to solve fluid-structure interaction (FSI) problems. FSI features in a vast range of physical systems and has a wide application in engineering. The work of this thesis is focused on the partitioned methods, mostly due to their features of modularity, robustness and reliability. In a partitioned approach, separate solvers are used for the fluid and structural sub-problem domains and a coupling method is devised to account for their mutual interaction. Moreover, the thesis is focused on FSI problems with strong added-mass effect, which are more challenging to solve numerically. For such FSI problems, normally an implicit partitioned method is used which enforces the coupling conditions on the interface through coupling iterations between the fluid and structural solvers. However, these methods are computationally expensive. In this work we follow a semi-implicit approach to develop stable, efficient and accurate numerical methods for FSI problems. In these methods, the fluid pressure term is segregated and strongly coupled to the structure via coupling iterations. However, the remaining fluid terms and the geometrical nonlinearities are treated explicitly. Strong coupling of the fluid pressure term provides for the stability of the method in FSI problems with strong added-mass effect, while loose coupling of the remaining terms reduces the computational cost of the simulations. The work of this thesis could be divided into three major parts. In the first part, we have developed a simple, efficient and robust semi-implicit coupling method for FSI problems with strong added-mass effect. The proposed method is simple and modular. An extensive set of numerical tests were carried out and the results were compared both to literature data (numerical and experimental), as well as domestic results obtained by using a fully-implicit coupling method. Results showed that the proposed method considerably reduces the computational cost of the simulations without degrading the stability or accuracy of the solution. Moreover, the robustness of the method is demonstrated through numerical tests. Furthermore, we have tried to further analyze the semi-implicit methods in order to gain a better understanding of several unaddressed issues concerning different aspects of these methods. The second major part of this thesis is focused on the temporal accuracy of the semi-implicit coupling methods for FSI problems. The semi-implicit methods in the literature appear to be only first-order in time. Most semi-implicit methods rely on using a projection method for the fluid equations, while extending the temporal accuracy of the projection methods is not straightforward. Moreover, mesh-conforming FSI solution methods require solving the ALE form of the Navier-Stokes equations on a moving mesh, which does not necessarily preserve the order of accuracy of the method on a fixed grid. Furthermore, if the FSI coupling technique is not properly designed, the second-order accuracy for the coupled problem is not guaranteed, even though each sub-problem possessed such accuracy. In this work, we have proposed a second-order time accurate semi-implicit method for FSI problems and demonstrated its second-order accuracy through rigorous numerical tests. The last major part of this thesis is concerned with computational efficiency and parallel scalability of the developed methods for numerical solution of complex FSI problems on massively-parallel supercomputers. We have presented a scalable parallel framework for partitioned solution of FSI problems through multi-code coupling. Two instances of our in-house software is used to solve the fluid and structural sub-problems. The communication between the single-physics solvers are carried out using an external coupling library. Parallel efficiency and scalability of the coupled framework is demonstrated in solving practical FSI test cases.Esta tesis está dedicada al desarrollo de métodos numéricos para resolver problemas de interacción de fluido-estructura (FSI). Esta fenomenología aparece en una amplia gama de sistemas físicos y aplicaciones en ingeniería. El trabajo se centra en los métodos de partición, principalmente debido a sus características de modularidad, robustez y fiabilidad. En estos métodos se utilizan solvers distintos para los dominios de fluido y estructura, siendo esencial la técnica de acoplamiento para tener en cuenta su interacción mutua. Además, la tesis se centra en los problemas del FSI con un fuerte efecto de "masa agregada", que son más complejos de resolver numéricamente. Normalmente se usa un método de partición implícito que impone las condiciones de acoplamiento en la interfaz a través de iteraciones entre los solucionadores de fluido y de estructura. Sin embargo, estos métodos son computacionalmente costosos. En esta tesis seguimos un enfoque semi-implícito que permite métodos numéricos estables, eficientes y precisos, en donde el término de presión del fluido está segregado y fuertemente acoplado a la estructura a través de iteraciones de acoplamiento. Sin embargo, los términos fluidos restantes y las no linealidades geométricas se tratan explícitamente. El fuerte acoplamiento del término de presión del fluido proporciona la estabilidad del método en problemas de FSI con un fuerte efecto de masa agregada, mientras que el acoplamiento de los términos restantes reduce el coste computacional. La tesis se divide en tres partes principales. En la primera se desarrolla un método de acoplamiento semi-implícito eficiente y robusto para problemas con un fuerte efecto de masa agregada. El método propuesto es simple y modular. Se llevó a cabo un extenso conjunto de pruebas numéricas. Los resultados se compararon con datos de la literatura (numéricos y experimentales), así como con resultados propios obtenidos mediante el uso métodos de acoplamiento totalmente implícitos. Las pruebas realizadas mostraron que el método propuesto reduce considerablemente el coste computacional de las simulaciones sin degradar su estabilidad y precisión. Además, se ha analizado más a fondo los métodos semi-implícitos con el fin de obtener una mejor comprensión de varias cuestiones no abordadas en relación con algunos aspectos de estos métodos. La segunda parte de esta tesis se centra en la precisión temporal de los métodos de acoplamiento semi-implícitos para problemas de FSI. La mayoría de los métodos semi-implícitos propuestos se basan en el uso de técnicas de proyección para las ecuaciones del fluido, con aproximaciones de primer orden temporal, no siendo sencilla su extensión a alto orden. Además, los métodos de malla-conforme requieren la resolución ALE de las ecuaciones de Navier-Stokes en mallas en movimiento, lo que no necesariamente conserva el orden de precisión del método en una cuadrícula fija. Si la técnica de acoplamiento FSI no está diseñada adecuadamente, no se puede garantizar la precisión de segundo orden para el problema acoplado, aunque cada sub-problema posea tal precisión. En este trabajo se propone un método semi-implícito de segundo orden temporal para este tipo de problemas, y se demuestra dicha precisión a través de rigurosas pruebas numéricas. La última parte de esta tesis se refiere a la eficiencia computacional y la escalabilidad paralela de los métodos desarrollados para la solución numérica de problemas complejos de FSI en supercomputadoras masivamente paralelas. Se presenta un marco paralelo escalable para la solución particionada a través del acoplamiento de múltiples códigos. Se utilizan dos instancias de nuestro software interno para resolver los sub-problemas de fluidos y estructurales. La comunicación entre los solucionadores de física simple se realiza mediante una biblioteca de acoplamiento externa...Postprint (published version

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Fluid-Structure Interaction Problems in Hemodynamics:Parallel Solvers, Preconditioners, and Applications

In this work we aim at the description, study and numerical investigation of the fluid-structure interaction (FSI) problem applied to hemodynamics. The FSI model considered consists of the Navier-Stokes equations on moving domains modeling blood as a viscous incompressible fluid and the elasticity equation modeling the arterial wall. The fluid equations are derived in an arbitrary Lagrangian-Eulerian (ALE) frame of reference. Several existing formulations and discretizations are discussed, providing a state of the art on the subject. The main new contributions and advancements consist of: A description of the Newton method for FSI-ALE, with details on the implementation of the shape derivatives block assembling, considerations about parallel performance, the analytic derivation of the derivative terms for different formulations (conservative or not) and for different types of boundary conditions. The implementation and analysis of a new category of preconditioners for FSI (applicable also to more general coupled problems). The framework set up is general and extensible. The proposed preconditioners allow, in particular, a separate treatment of each field, using a different preconditioning strategy in each case. An estimate for the condition number of the preconditioned system is proposed, showing how preconditioners of this type depend on the coupling, and explaining the good performance they exhibit when increasing the number of processors. The improvement of the free (distributed under LGPL licence) parallel finite elements library LifeV. Most of the methods described have been implemented within this library during the period of this PhD and all the numerical tests reported were run using this framework. The simulation of clinical cases with patient-specific data and geometry, the comparison on simulations of physiological interest between different models (rigid, FSI, 1D), discretizations and methods to solve the nonlinear system. A methodology to obtain patient-specific FSI simulations starting from the raw medical data and using a set of free software tools is described. This pipeline from imaging to simulation can help medical doctors in diagnosis and decision making, and in understanding the implication of indicators such as the wall shear stress in the pathogenesis

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Aeronautical engineering: A cumulative index to a continuing bibliography (supplement 274)

This publication is a cumulative index to the abstracts contained in supplements 262 through 273 of Aeronautical Engineering: A Continuing Bibliography. The bibliographic series is compiled through the cooperative efforts of the American Institute of Aeronautics and Astronautics (AIAA) and the National Aeronautics and Space Administration (NASA). Seven indexes are included: subject, personal author, corporate source, foreign technology, contract number, report number, and accession number