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.

Two of the methods common in video game fluid simulation are SmoothedParticle Hydrodynamics (SPH), and Position Based Dynamics (PBD). They are both Lagrangian methods of fluid simulation. SPH has been used for many years in offline simulations and has truthful visuals, but is not as stable as the newer method PBD when using larger timesteps. SPH also tends to become unstable during compression. In this report both methods have been tested on different scenarios as the methods’ performance and visual depend on the scenario used. Additionally, the size of the particle radius was varied when comparing Compressible SPH (CSPH), Weak Compressible SPH (WCSPH), and PBD. From these tests, the conclusion could be drawn that CSPH performed slightly better than PBD regarding frames per second (FPS) in all cases except one. However, WCSPH and sometimes CSPH had stability issues. The stability of PBD and its possibility for larger timesteps with only minor FPS difference lead to the conclusion that PBD is overall the more suitable method for fluid simulation in video games. / Två av metoderna som är vanliga vid vätskesimulering i videospel är SmoothedParticle Hydrodynamics (SPH) och Position Based Dynamics (PBD). De är båda Lagrangiska metoder för vätskesimulering. SPH har använts i många år i offline-simuleringar och har realistiskt utseende, men är inte lika stabil som den nyare metoden PBD vid användning av större tidssteg. SPH tenderar också att bli instabil under kompression. Båda metoderna blev testade i olika scenarion eftersom deras prestanda och utseende beror på det använda scenariot. Storleken av partikelradien har också varierat när Compressible SPH (CSPH), Weak Compressible SPH (WCSPH) och PBD jämfördes. Från dessa tester kunde man se att CSPH presterade lite bättre än PBD gällande bilder per sekund (FPS) i alla fall utom ett. Däremot hade WCSPH och ibland CSPH stabilitetsproblem. Stabiliteten av PBD och dess möjlighet att ta större tidssteg med endast minimala FPS skillnader ledde till slutsatsen att PBD är överlag den mer lämpliga metoden för vätskesimulering i videospel.