Integral Methods for Versatile Fluid Simulation

Abstract

Physical simulations of natural phenomena usually boil down to solving an ordinary or partial differential equation system. Partial differential equation systems can be formulated either in differential form or in integral form. This dissertation explores integral methods for the simulation of magnetic fluids, so-called ferrofluids, and the surface of the vast ocean. The first two parts of this dissertation aim to contribute to the development of accurate and efficient methods for simulating ferrofluids on the macroscopic (in the order of millimeters) scale. The magnetic nature of these fluids imposes challenges for the simulation. The two most important challenges are to first model the influence of ferrofluids on surrounding magnetic fields and second the influence of magnetic forces on the fluids’ dynamics. To tackle these challenges, two Lagrangian simulation methods have been proposed. The first method discretizes the magnetic substance as clusters of particles carrying radial basis functions and applies magnetic forces between these particles. This is a mesh-free method suitable for particle-based fluid simulation frameworks such as smoothed-particle hydrodynamics. The second method follows another direction, only discretizing the fluid’s surface as triangles and vertices. A surface-based simulation for the fluid part is employed, and a boundary element method is utilized for the magnetic part. The magnetic forces are added as gradients of the magnetic energy defined on the fluid’s surface. The second approach has to solve significantly fewer unknowns in the underlying equations, and uses a more accurate surface tension model compared to the radial basis function approach. The proposed methods are able to reproduce a series of characteristic phenomena of magnetic fluids, both qualitatively and in some cases even quantitatively which leads to a better understanding of such kind of materials. The boundary element method employed in the second part shows advantages beyond ferrofluids. In the third part of this thesis, a boundary element method is coupled with a particle-based fluid simulator for ocean simulation. The wavy motion of the ocean is simulated using large triangle meshes, while water splashes are simulated using particles. This approach is much more efficient in terms of computation time and memory consumption.