Studying free surface flows generated by a moving body is relevant to various fluid-structure interaction applications. Such investigations are crucial for fields such as ship and submarine design and wave energy devices, where understanding fluid dynamics and wave motion is essential. Although many problems involve bodies moving at constant speed in water, wave generation by submerged structures remains a longstanding challenge. Despite decades of research, progress in this area remains limited. Meanwhile, advances in high-performance computing have enabled CFD methods of increasing fidelity for predicting flows. This thesis presents a new high-order numerical solver capable of finding steady-state solutions to the incompressible Navier-Stokes equations subject to various flow conditions, different submerged structures, and a free surface. With this objective, the mathematical task is twofold: determine i) the final shape of the free surface and ii) the flow quantities, including velocity and pressure. The governing equations are handled within the open-source parallel computational framework, Firedrake, where they are solved considering a Galerkin-based numerical discretization. In particular, the weak form of the problem is addressed using a spectral element method (SEM). Curvilinear elements are introduced to enable the solver to accurately represent and handle more complex geometries in the setting of a high-order spectral element method. Since the free surface dynamically adapts to the pressure and velocity fields of the flow, an iterative approach is employed to reach the steady-state profile. The proposed spectral element solver is first validated by solving intermediate problem, then is subsequently extended to account for free surface effects. The resulting steady wave patterns generated by a submerged moving body are analyzed under various flow conditions. The numerical results are qualitatively compared with reference studies and with a solution obtained using a finite-volume CFD code (OpenFOAM). Finally, the model is extended to three spatial dimensions in order to simulate scenarios that are representative of real-world applications.
Lo studio dei flussi a superficie libera generati da un corpo in movimento è rilevante per numerose applicazioni nell’ambito dell’interazione fluido-struttura. Tali indagini sono fondamentali in settori come la progettazione di navi e sottomarini o dei dispositivi per il recupero dell’energia dalle onde, dove la comprensione della dinamica dei fluidi e del moto ondoso è essenziale. Sebbene molti problemi coinvolgano corpi sommersi che si muovono a velocità costante, lo studio delle onde da essi generate rimane ancora oggi un problema complesso. Nonostante decenni di studi, i recenti progressi in questo ambito sono stati limitati. Tuttavia, lo sviluppo del calcolo ad alte prestazioni ha reso accessibili metodi CFD più avanzati e accurati. Questa tesi presenta un nuovo risolutore numerico ad alto ordine in grado di calcolare soluzioni stazionarie delle equazioni di Navier-Stokes incomprimibili, considerando diverse condizioni di flusso, strutture sommerse e la presenza di una superficie libera. L’obiettivo matematico si articola in due compiti principali: determinare i) la forma finale della superficie libera e ii) le grandezze del flusso, come velocità e pressione. Le equazioni di governo sono risolte all’interno del framework computazionale open-source Firedrake, utilizzando una discretizzazione numerica basata sul metodo di Galerkin. In particolare, la forma debole del problema viene affrontata mediante un metodo agli elementi spettrali (SEM). Vengono introdotti elementi curvilinei per poter rappresentare e gestire con precisione geometrie più complesse. Poiché la superficie libera si adatta dinamicamente ai campi di pressione e velocità del flusso, si adotta un approccio iterativo per raggiungere un profilo stazionario. Il risolutore proposto viene dapprima validato risolvendo problemi intermedi; successivamente, è esteso per tenere conto degli effetti di superficie libera. I profili d’onda generati da un corpo in movimento sommerso sono esaminati sotto diverse condizioni di flusso. I risultati numerici sono confrontati qualitativamente con studi di riferimento e con una soluzione ottenuta utilizzando un codice CFD a volumi finiti (OpenFOAM). Infine, il modello è esteso a tre dimensioni al fine di simulare scenari più realistici.
A high-order steady-state solver for free surface flow problems
MINNITI, SIMONE
2024/2025
Abstract
Studying free surface flows generated by a moving body is relevant to various fluid-structure interaction applications. Such investigations are crucial for fields such as ship and submarine design and wave energy devices, where understanding fluid dynamics and wave motion is essential. Although many problems involve bodies moving at constant speed in water, wave generation by submerged structures remains a longstanding challenge. Despite decades of research, progress in this area remains limited. Meanwhile, advances in high-performance computing have enabled CFD methods of increasing fidelity for predicting flows. This thesis presents a new high-order numerical solver capable of finding steady-state solutions to the incompressible Navier-Stokes equations subject to various flow conditions, different submerged structures, and a free surface. With this objective, the mathematical task is twofold: determine i) the final shape of the free surface and ii) the flow quantities, including velocity and pressure. The governing equations are handled within the open-source parallel computational framework, Firedrake, where they are solved considering a Galerkin-based numerical discretization. In particular, the weak form of the problem is addressed using a spectral element method (SEM). Curvilinear elements are introduced to enable the solver to accurately represent and handle more complex geometries in the setting of a high-order spectral element method. Since the free surface dynamically adapts to the pressure and velocity fields of the flow, an iterative approach is employed to reach the steady-state profile. The proposed spectral element solver is first validated by solving intermediate problem, then is subsequently extended to account for free surface effects. The resulting steady wave patterns generated by a submerged moving body are analyzed under various flow conditions. The numerical results are qualitatively compared with reference studies and with a solution obtained using a finite-volume CFD code (OpenFOAM). Finally, the model is extended to three spatial dimensions in order to simulate scenarios that are representative of real-world applications.File | Dimensione | Formato | |
---|---|---|---|
2025_07_Minniti_ExecutiveSummary_02.pdf
accessibile in internet per tutti
Descrizione: Executive summary
Dimensione
49.47 MB
Formato
Adobe PDF
|
49.47 MB | Adobe PDF | Visualizza/Apri |
2025_07_Minniti_Tesi_01.pdf
accessibile in internet per tutti
Descrizione: Tesi
Dimensione
356.24 MB
Formato
Adobe PDF
|
356.24 MB | Adobe PDF | Visualizza/Apri |
I documenti in POLITesi sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/10589/240962