This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

This thesis presents an automatic animation system for jellyfish that is based on a physical simulation of the organism and its surrounding fluid. Our goal is to explore the unusual style of locomotion, namely jet propulsion, which is utilized by jellyfish. The organism achieves this propulsion by contracting its body, expelling water, and propelling itself forward. The organism then expands again to refill itself with water for a subsequent stroke. We endeavor to model the thrust achieved by the jellyfish, and also the evolution of the organism's geometric configuration. <p> We restrict our discussion of locomotion to fully grown adult jellyfish, and we restrict our study of locomotion to the resonant gait, which is the organism's most active mode of locomotion, and is characterized by a regular contraction rate that is near one of the creature's resonant frequencies. We also consider only species that are axially symmetric, and thus are able to reduce the dimensionality of our model. We can approximate the full 3D geometry of a jellyfish by simulating a 2D slice of the organism. This model reduction yields plausible results at a lower computational cost. From the 2D simulation, we extrapolate to a full 3D model. To prevent our extrapolated model from being artificially smooth, we give the final shape more variation by adding noise to the 3D geometry. This noise is inspired by empirical data of real jellyfish, and also by work with continuous noise functions from the graphics community. <p> Our 2D simulations are done numerically with ideas from the field of computational fluid dynamics. Specifically, we simulate the elastic volume of the jellyfish with a spring-mass system, and we simulate the surrounding fluid using the semi-Lagrangian method. To couple the particle-based elastic representation with the grid-based fluid representation, we use the immersed boundary method. We find this combination of methods to be a very efficient means of simulating the 2D slice with a minimal compromise in physical accuracy.

Dans cette thèse, nous présentons et étudions une nouvelle formulation du problème de contact frottant entre deux corps élastiques se basant sur la méthode de Nitsche. Dans cette méthode les conditions de contact sont imposées faiblement, grâce à un terme additionnel consistant et stabilisé par un paramètre gamma. En premier lieu, nous introduisons, l’étude effectuée en petites déformations pour une version non biaisée de la méthode. La non-distinction entre une surface maître et une surface esclave permettera à la méthode d’être plus générique et applicable directement au problème d’auto-contact. Le cadre restrictif des petites déformations nous permet d’obtenir des résultats théoriques sur la stabilité et la convergence de la méthode. Ces résultats sont complétés par une validation numérique. Ensuite, nous introduisons l’extension de la méthode de Nitsche au cadre des grandes déformations qui est d’avantage pertinent pour les applications industrielles et les situations d’auto-contact. La méthode de Nitsche est formulée pour un matériau hyper-élastique avec frottement de Coulomb et se décline en deux versions : biaisée ou non. La formulation est généralisée à travers un paramètre theta pour couvrir toute une famille de méthodes. Chaque variante particulière a des propriétés différentes du point de vue théorique et numérique, en termes de précision et de robustesse. La méthode est testée et validée à travers plusieurs cas tests académiques et industriels. Nous effectuons aussi une étude de l’influence de l’intégration numérique sur la précision et la convergence de la méthode. Cette étude couvre une comparaison entre plusieurs schémas d’intégration proposés dans la littérature pour d’autres méthodes intégrales. / In this thesis, we present and study a new formulation of frictional contact between two elastic bodies based on Nitsche’s method. This method aims to treat the interface conditions in a weak sense, thanks to a consistent additional term stabilized with the parameter gamma. At first, we introduce the study carried out in the small strain framwork for an unbiased version of the ethod. The non-distinction between a master surface and a slave one will allow the method to be more generic and directly applicable to the self-contact problem. The restrictive framework of small strain allowed us to obtain theoretical results on the consistency and convergence of the method. Then, we present the extension of the Nitsche method to the large strain case more relevant for industrial applications and situations of self-contact. This Nitsche’s method is formulated for an hyper-elastic material and declines in the two versions: biased and unbiased. We describe a class of methods through a generalisation parameter theta . Particular variants have different properties from a numerical point of view, in terms of accuracy and robustness. To prove the accuracy of the method for large deformations, we provide several academic and industrial tests. We also study the influence of numerical quadrature on the accuarcy and convergence of the method. This study covers a comparison of several integration rules proposed in the literature for other integral methods.

In order to elucidate the progression mechanism of cavitation erosion, the behaviors of a single cavitation bubble collapse near a pit on a wall and both the resulting pressure wave in fluid and stress wave in material are investigated in detail. To find out the mechanism of cavitation erosion, many experimental studies on the bubble collapse behavior near a flat rigid wall and the resulting material damage have been conducted so far. A lot of numerical studies using only fluid analysis have been also carried out. In recent years, a few studies on the bubble collapse near a more complex geometry were made and it is reported that more complex geometry has an effect on the bubble collapse behavior, jet formation and subsequent wave dynamics. It is, however, very challenging to introduce a material analysis and investigate detailed stress wave propagation in the material and its effect on the material damage i.e. cavitation erosion. This study tackles this problem using an in-house fluid/material two-way coupled numerical analysis method which considers reflection and transmission of plane waves with acoustic impedance at the fluid/material boundary. In the fluid domain, the locally homogeneous model of compressible gas-liquid two-phase medium is used for capturing the gas-liquid interface. The compressibility of two-phase flow is also considered in this model so that the propagation of pressure wave can be also be taken into account. The governing equations are the 3D compressible gas-liquid two-phase Navier-Stokes equations. In the material domain, the governing equations are composed of the motion equations and the time-differential constitutive equations assuming that the material is a homogeneous isotropic elastic medium, which can simulate the stress wave propagation in the material. Results show that the stress waves are concentrated at the bottom of the pit regardless of the initial bubble position. It is also found that the surface pressure in the fluid side does not necessarily correlate with the stresses in the material, suggesting the importance of material analysis. Moreover, under high pressure conditions, a rapid bubble collapse causes a gas phase generation at the bottom of the pit and its gas phase is contracted and collapsed by the pressure wave, which leads to pressure and stress peaks at the bottom of the pit. Furthermore, through the study of the effect of initial bubble position on its collapse behavior, it is confirmed that, when the initial bubble position is shifted horizontally, bubble collapses asymmetrically and the pressure waves tend to be directed away from a pit. This research numerically reveals that a single bubble collapse near a pit on a wall results in high strain energy concentration at the bottom of the pit, which gives rise to deeper erosion progression at the bottom of the pit. / För att klargöra framstegsmekanismen för kavitationserosion kollapsar beteendet hos en enda kavitationsbubbla nära en grop på en vägg och både den resulterande tryckvågen i vätska och stressvåg i material undersöks i detalj. För att ta reda på mekanismen för kavitationserosion har många experimentella studier av bubblans kollapsbeteende nära en platt styv vägg och den resulterande materialskada genomförts hittills. Många numeriska studier med endast vätskeanalys har också genomförts. Under de senaste åren gjordes några studier om bubblans kollaps nära en mer komplex geometri och det rapporteras att mer komplex geometri har en effekt på bubblans kollapsbeteende, strålbildning och efterföljande vågdynamik. Det är dock mycket utmanande att införa en materialanalys och undersöka detaljerad spänningsvågförökning i materialet och dess inverkan på materialskadorna, dvs. kavitationserosion. Denna studie hanterar detta problem med hjälp av en inbyggd tvåvägs kopplad numerisk analysmetod som tar hänsyn till reflektion och överföring av plana vågor med akustisk impedans vid vätska / materialgränsen. I fluiddomänen används den lokalt homogena modellen av tvåfasmedium för komprimerbar gas-vätska för att fånga gas-vätskegränssnittet. Komprimerbarheten av tvåfasflöde beaktas också i denna modell så att utbredningen av tryckvågen också kan beaktas. De styrande ekvationerna är de 3D-komprimerbara tvåfasiga gasvätska Navier-Stokes-ekvationerna. I materialdomänen är de styrande ekvationerna sammansatta av rörelseekvationer och tidsdifferentialkonstitutiva ekvationer förutsatt att materialet är ett homogent isotropiskt elastiskt medium, vilket kan simulera spänningsvågutbredningen i materialet. Resultaten visar att stressvågorna är koncentrerade längst ner i gropen oavsett den ursprungliga bubbelpositionen. Man har också funnit att yttrycket i vätskesidan inte nödvändigtvis korrelerar med spänningarna i materialet, vilket tyder på vikten av materialanalys. Vidare orsakar en snabb bubbelskollaps under högtrycksförhållanden en gasfasgenerering vid botten av gropen och dess gasfas dras samman och kollapsas av tryckvågen, vilket leder till tryck och spänningstoppar vid botten av gropen. Vidare bekräftas det genom studien av effekten av den ursprungliga bubbelpositionen på dess kollapsbeteende att när den ursprungliga bubbelpositionen förskjuts horisontellt kollapsar bubblan asymmetriskt och tryckvågorna tenderar att riktas bort från en grop. Denna undersökning avslöjar numeriskt att en enda bubbla kollapsar nära en grop på en vägg resulterar i hög spänningsenergikoncentration längst ner i gropen, vilket ger upphov till djupare erosionsprogression längst ner i gropen.