We present a series of 2D and 3D breaking wave animations to demonstrate the power of the method.
An additional advantage of the method is that it provides a significantly faster method for obtaining the full 3D breaking wave evolution compared to starting the simulation at an early stage and using solely the 3D Navier-Stokes equations. The animator is thus enabled to obtain a full animation of a breaking wave while controlling the shape and the timing of the breaking. The wave dynamics previous to the moment the animator exerts control can also be generated based on the wave library. Our system computes then the subsequent dynamics with the aid of a 3D Navier-Stokes solver. In our Slice Method framework an animator defines the shape of a breaking wave at a desired moment in its evolution based on a library of breaking waves. In this paper we develop a novel fluid animation control approach and we present its application to controlling breaking waves. Applications are presented for incompressible flow in 3D, where pairs of thin vortex rings interact and, in some cases, merge.Ĭontrolling fluids is still an open and challenging problem in fluid animation. Since only a fixed grid is used with local variables, the vorticity confinement method is quite general and can automatically accommodate changes in vortex topology, such as merging. The discretized Euler equations with the extra term can be solved on fairly coarse, Eulerian computational grids with simple low-order (first- or second-) accurate numerical methods, but will still yield concentrated vortices which convect without spreading due to numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. The partial differential equations with this extra term admit solutions that consist of Lagrangian-like confined vortical regions, or covons, in the shape of two-dimensional (2-D) vortex ‘‘blobs’’ and three-dimensional (3-D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. This term depends only on local variables and is zero outside vortical regions.
Results show that, although the RLE-based simulator can take several times longer than the current simulator to complete a given simulation, the memory usage is significantly reduced, making an RLE-based simulation preferable in a few specific circumstances.Ī new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. The modified LBM is implemented within the open-source 3D animation package Blender and compared to Blender's current LBM simulator using the metrics of memory usage and time required to complete a given simulation. This thesis modifies the LBM to utilize a recursive run-length-encoded (RLE) grid data structure instead of the standard fixed array of grid cells, which reduces the amount of memory required for LBM simulations as well as allowing the domain to grow and shrink as necessary to accomodate a liquid surface.
Unfortunately, current LBM simulations also suffer from high memory usage and restrict free surface fluids to domains of fixed size. The Lattice-Boltzmann Method (LBM) is one fluid simulation technique that has gained recent popularity due to its relatively simple basic algorithm and the ease with which it can be distributed across multiple processors.
Much of this imagery needs to be as realistic as possible, and animators have turned to techniques such as fluid simulation to create scenes involving substances like smoke, fire, and water. Computer-generated imagery is ubiquitous in today's society, appearing in advertisements, video games, and computer-animated movies among other places.