Oggigiorno, modelli matematici e simulazioni numeriche sono ampiamente utilizzati nell’intero campo della ricerca fluidodinamica. Essi rappresentano una potente risorsa per comprendere meglio i fenomeni e i processi e per ridurre significativamente i costi che sarebbero altrimenti necessari per la realizzazione di esperimenti di laboratorio (a volte anche per ottenere utili dati che non potrebbero essere raccolti mediante misurazioni). Attualmente esistono molte importanti industrie di sistemi idraulici che, per la corretta analisi del comportamento dei sistemi progettati, richiedono l’uso preventivo di un accurato modello matematico, in grado di descrivere l’andamento delle proprietà del fluido nelle tubazioni. D’altra parte, la disponibilità di strumenti matematici robusti ed efficienti, insieme al know-how ingegneristico nel settore della fluidodinamica, rappresenta uno strumento inestimabile per un supporto costante anche negli studi emodinamici, fornendo approcci pratici per la quantificazione delle variabili coinvolte nella fluidodinamica cardiovascolare. La corretta caratterizzazione delle interazioni tra il fluido e la parete che ne circoscrive il moto, è un aspetto fondamentale in tutti i contesti di condotte deformabili, che richiede la massima attenzione in ogni fase dello sviluppo dello schema di calcolo e della interpretazione dei risultati e nella loro applicazione a casi di interesse pratico. In questa Tesi di Dottorato vengono presentati innovativi modelli matematici in grado di prevedere il comportamento del meccanismo di interazione fluido-struttura che sta alla base della dinamica dei flussi in diverse condotte deformabili. Partendo dal settore dell’ingegneria puramente civile, con lo studio di condotte idrauliche in plastica, l’applicazione finale dello strumento proposto è legata al campo della ricerca medica, per riprodurre la meccanica del flusso sanguigno sia nelle arterie che nelle vene. A tal fine, sono stati applicati ed estesi diversi modelli viscoelastici lineari, dai più semplici ai più sofisticati, per ottenere sistemi aumentati di interazione fluido-struttura in cui l’equazione costitutiva del materiale è direttamente inserita nel sistema come equazione alle derivate parziali. Questi sistemi sono risolti ricorrendo a Metodi ai Volumi Finiti al secondo ordine che tengono conto della recente evoluzione della letteratura computazionale dei sistemi iperbolici di leggi di bilancio. I modelli sono stati ampiamente validati attraverso diversi tipi di casi test, evidenziando i vantaggi dell’utilizzo del sistema di equazioni in forma aumentata. I risultati numerici sono stati confrontati con soluzioni quasi esatte di problemi ideali dipendenti dal tempo per situazioni vicine alla realtà o con valori di riferimento ottenuti con schemi numerici adottati solitamente nello specifico campo di ricerca indagato. Inoltre, sono stati presi in considerazione confronti con dati sperimentali sia per lo scenario delle condotte idriche che per la modellazione del flusso sanguigno, ricorrendo a misurazioni in-vivo ad hoc per quest’ultimo. Sono state effettuate analisi di accuratezza ed efficienza in diversi contesti, nonché un’analisi di sensitività per quanto riguarda la parte finale del progetto, relativa ad uno studio più applicativo sull’ipertensione arteriosa.

Nowadays, mathematical models and numerical simulations are widely used in the whole fluid dynamics research field. They represent a powerful resource to better understand phenomena and processes and to significantly reduce the costs that would otherwise be necessary for carrying out laboratory experiments (sometimes even allowing to obtain useful data that could not be collected by measurements). Currently there are many important industries of hydraulic systems which, for the correct analysis of the behavior of the designed systems, require the preventive use of an accurate mathematical model, able to describe the trend of the properties of the fluid in the pipelines. On the other hand, the availability of robust and efficient mathematical instruments, together with the engineering know-how in the fluid mechanics sector, represents an invaluable tool for a consistent support even in hemodynamics studies, providing practical approaches for the quantification of variables involved in the cardiovascular fluid dynamics. The correct characterization of the interactions occurring between the fluid and the wall that circumscribes the motion of the fluid itself, is a fundamental aspect in all the contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational scheme and the interpretation of the results and at their application to cases of practical interest. In this PhD Thesis, innovative mathematical models able to predict the behavior of the fluid-structure interaction mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented fluid-structure interaction systems in which the constitutive equation of the material is directly inserted into the system as partial differential equation. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Numerical results have been compared with quasi-exact solutions of idealized time-dependent tests for situations close to reality or with reference values obtained with numerical schemes generally adopted in the specific research field investigated. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to ad hoc in-vivo measurements for the latter. Accuracy and efficiency analyses have been performed in different contexts, as well as a sensitivity analysis with regards to the final part of the project, related to a more applicative study on arterial hypertension.

1D augmented fluid-structure interaction systems with viscoelasticity: from water pipelines to blood vessels

BERTAGLIA, Giulia
2020-03-19T00:00:00+01:00

Abstract

Nowadays, mathematical models and numerical simulations are widely used in the whole fluid dynamics research field. They represent a powerful resource to better understand phenomena and processes and to significantly reduce the costs that would otherwise be necessary for carrying out laboratory experiments (sometimes even allowing to obtain useful data that could not be collected by measurements). Currently there are many important industries of hydraulic systems which, for the correct analysis of the behavior of the designed systems, require the preventive use of an accurate mathematical model, able to describe the trend of the properties of the fluid in the pipelines. On the other hand, the availability of robust and efficient mathematical instruments, together with the engineering know-how in the fluid mechanics sector, represents an invaluable tool for a consistent support even in hemodynamics studies, providing practical approaches for the quantification of variables involved in the cardiovascular fluid dynamics. The correct characterization of the interactions occurring between the fluid and the wall that circumscribes the motion of the fluid itself, is a fundamental aspect in all the contexts involving deformable ducts, which requires the utmost attention at every stage of both the development of the computational scheme and the interpretation of the results and at their application to cases of practical interest. In this PhD Thesis, innovative mathematical models able to predict the behavior of the fluid-structure interaction mechanism that underlies the dynamics of flows in different compliant ducts is presented. Starting from the purely civil engineering sector, with the study of plastic water pipelines, the final application of the proposed tool is linked to the medical research field, to reproduce the mechanics of blood flow in both arteries and veins. With this aim, various linear viscoelastic models, from the simplest to the more sophisticated, have been applied and extended to obtain augmented fluid-structure interaction systems in which the constitutive equation of the material is directly inserted into the system as partial differential equation. These systems are solved recurring to second-order Finite Volume Methods that take into account the recent evolution in the computational literature of hyperbolic balance laws systems. The models have been extensively validated through different types of test cases, highlighting the advantages of using the augmented formulation of the system of equations. Numerical results have been compared with quasi-exact solutions of idealized time-dependent tests for situations close to reality or with reference values obtained with numerical schemes generally adopted in the specific research field investigated. Furthermore, comparisons with experimental data have been considered both for the water pipelines scenario and the blood flow modeling, recurring to ad hoc in-vivo measurements for the latter. Accuracy and efficiency analyses have been performed in different contexts, as well as a sensitivity analysis with regards to the final part of the project, related to a more applicative study on arterial hypertension.
VALIANI, Alessandro
CALEFFI, Valerio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11392/2488143
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