We describe a new approach for the purely Eulerian simulation of incompressible fluids. In it, the fluid state is represented by a C 2 -valued wave function evolving under the Schrödinger equation subject to incompressibility constraints. The underlying dynamical system is Hamiltonian and governed by the kinetic energy of the fluid together with an energy of Landau-Lifshitz type. The latter ensures that dynamics due to thin vortical structures, all important for visual simulation, are faithfully reproduced. This enables robust simulation of intricate phenomena such as vortical wakes and interacting vortex filaments, even on modestly sized grids. Our implementation uses a simple splitting method for time integration, employing the FFT for Schrödinger evolution as well as constraint projection. Using a standard penalty method we also allow arbitrary obstacles. The resulting algorithm is simple, unconditionally stable, and efficient. In particular it does not require any Lagrangian techniques for advection or to counteract the loss of vorticity. We demonstrate its use in a variety of scenarios, compare it with experiments, and evaluate it against benchmark tests. A full implementation is included in the ancillary materials.

Abstract Fluid simulation plays a key role in various domains of science including computer graphics. While most existing work addresses fluids on bounded Euclidean domains, we consider the problem of simulating the behavior of an incompressible fluid on a curved surface represented as an unstructured triangle mesh. Unlike the commonly used Eulerian description of the fluid using its time‐varying velocity field, we propose to model fluids using their vorticity, i.e., by a (time varying) scalar function on the surface. During each time step, we advance scalar vorticity along two consecutive, stationary velocity fields. This approach leads to a variational integrator in the space continuous setting. In addition, using this approach, the update rule amounts to manipulating functions on the surface using linear operators, which can be discretized efficiently using the recently introduced functional approach to vector fields. Combining these time and space discretizations leads to a conceptually and algorithmically simple approach, which is efficient, time‐reversible and conserves vorticity by construction. We further demonstrate that our method exhibits no numerical dissipation and is able to reproduce intricate phenomena such as vortex shedding from boundaries.

We give an algorithm which extracts vortex filaments ("smoke rings") from a given 3D velocity field. Given a filament strength h > 0, an optimal number of vortex filaments, together with their extent and placement, is given by the zero set of a complex valued function over the domain. This function is the global minimizer of a quadratic energy based on a Schrödinger operator. Computationally this amounts to finding the eigenvector belonging to the smallest eigenvalue of a Laplacian type sparse matrix. Turning traditional vector field representations of flows, for example, on a regular grid, into a corresponding set of vortex filaments is useful for visualization, analysis of measured flows, hybrid simulation methods, and sparse representations. To demonstrate our method we give examples from each of these.

We show that the motion of rigid bodies under water can be realistically simulated by replacing the usual inertia tensor and scalar mass by the so-called Kirchhoff tensor. This allows us to model fluid-body interaction without simulating the surrounding fluid at all. We explain some of the phenomena that arise and compare our results against real experiments. It turns out that many real scenarios (sinking bodies, balloons) can be matched using a single, hand-tuned scaling parameter. We describe how to integrate our method into an existing physics engine, which makes underwater rigid body dynamics run in real time.

Simulating fluids based on vortex filaments is highly attractive for the creation of special effects because it gives artists full control over the simulation using familiar tools like curve editors or the scripted generation of new vortex filaments over time. Because filaments offer a very compact description of fluid flow, real time applications like games or virtual reality are also possible. We present a complete model that includes moving obstacles with vortex shedding, all represented as filaments. Due to variational reconnection the long-time behavior of our method is excellent: Energy and momentum stay constant within reasonable bounds and computational complexity does not increase over time.

We introduce jReality, a Java library for creating real-time interactive audiovisual applications with three-dimensional computer graphics and spatialized audio. Applications written for jReality will run unchanged on software and hardware platforms ranging from desktop machines with a single screen and stereo speakers to immersive virtual environments with motion tracking, multiple screens with 3D stereo projection, and multi-channel audio.