Category: Fluids

Recently, many techniques using computational fluid dynamics have been proposed for the simulation of natural phenomena such as smoke and fire. Traditionally, a single grid is used for computing the motion of fluids. When an object interacts with a fluid, the resolution of the grid must be sufficiently high because the shape of the object is represented by a shape sampled at the grid points. This increases the number of grid points that are required, and hence the computational cost is increased. To address this problem, we propose a method using multiple grids that overlap with each other. In addition to a large single grid (a global grid) that covers the whole of the simulation space, separate grids (local grids) are generated that surround each object. The resolution of a local grid is higher than that of the global grid. The local grids move according to the motion of the objects. Therefore, the process of resampling the shape of the object is unnecessary when the object moves. To accelerate the computation, appropriate resolutions are adaptively-determined for the local grids according to their distance from the viewpoint. Furthermore, since we use regular (orthogonal) lattices for the grids, the method is suitable for GPU implementation. This realizes the real-time simulation of interactions between objects and smoke.

A Fast Simulation Method Using Overlapping Grids for Interactions between Smoke and Rigid Objects

 We perform a detailed flop and bandwidth analysis of Jos Stam’s Stable Fluids algorithm on the CPU, GPU, and Cell. In all three cases, we find that the algorithm is bandwidth bound, with the cores sitting idle up to 96% of the time. Knowing this, we propose two modifications to accelerate the algorithm. First, a Mehrstellen discretization for the pressure solver which reduces the running time of the solver by a third. Second, a static caching scheme that eliminates roughly 99% of the random lookups in the advection stage. We observe a 2x speedup in the advection stage using this scheme. Both modifications apply equally well to all three architectures.

Hardware-Aware Analysis and Optimization of Stable Fluids

Grid-based methods have difficulty resolving features on or below the scale of the underlying grid. Although adaptive methods (e.g. RLE, octrees) can alleviate this to some degree, separate techniques are still required for simulating small-scale phenomena such as spray and foam, especially since these more diffuse materials typically behave quite differently than their denser counterparts. In this paper, we propose a two-way coupled simulation framework that uses the particle level set method to efficiently model dense liquid volumes and a smoothed particle hydrodynamics (SPH) method to simulate diffuse regions such as sprays. Our novel SPH method allows us to simulate both dense and diffuse water volumes, fully incorporates the particles that are automatically generated by the particle level set method in under-resolved regions, and allows for two way mixing between dense SPH volumes and grid-based liquid representations.

Two-Way Coupled SPH and Particle Level Set Fluid Simulation

In 2D, incompressible flows, the Stokes equations that represent the dynamics of very viscous flows and vorticity formulation of hydrodynamic equations both reduce to a scalar stream-function representation in terms of elliptic equations. By making use of this simplification and the properties of Fourier space representation of elliptic equations, we use a common spectral method to solve both of these equations. Based on this system of equations, we propose a level set based input description which provides a flexible environment for the user to model a wide range of flows and artistic effects in 2D. This input type allows the modeling of vortex sheet patterns and other complex flows with a very practical approach and chaotic, dynamic flows, even with viscous Stokes equations. A user interface is developed for the level set input which allows the user to draw the strokes or edit the level set data by applying transformation functions or perturbations. To sum up, this model can be used for the simulation of very viscous flows, vorticity dynamics, vortex sheet patterns, turbulent and chaotic flows as well as other artistic effects such as the traditional marbling patterns, with a simple, fast and stable system at high resolutions.

Level Set Driven Flows

We propose a novel method of controlling a multi-phase fluid so that it flows into a target shape in a natural way. To preserve the sharp detail of the target shape, we represent it as an implicit function and construct the level-set of that function. Previous approaches add the target-driven control force as an external term, which then becomes attenuated during the velocity projection step, making the convergence process unstable and causing sharp detail to be lost from the target shape. But we calculate the force on the fluid from the pressure discontinuity at the interface between phases, and integrate the control force into the projection step so as to preserve its effect. The control force is calculated using an enhanced version of the ghost fluid method (GFM), which guarantees that the fluid flows from the source shape and converges into the target shape, while achieving a more natural animation than other approaches. Our control force is merged during the projection step avoiding the need for a post-optimization process to eliminate divergence at the liquid interface. This makes our method easy to implement using existing fluid engines and it incurs little computational overhead. Experimental results show the accuracy and robustness of this technique.

Target-driven liquid animation with interfacial discontinuities

This paper describes a motion blur technique which can be applied to rendering fluid simulations that are carried out in the Eulerian framework. Existing motion blur techniques can be applied to rigid bodies, deformable solids, clothes, and several other kinds of objects, and produce satisfactory results. As there is no specific reason to discriminate fluids from the above objects, one may consider applying an existing motion blur technique to render fluids. However, here we show that existing motion blur techniques are intended for simulations carried out in the Lagrangian framework, and are not suited to Eulerian simulations. Then, we propose a new motion blur technique that is suitable for rendering Eulerian simulations.

Eulerian Motion Blur

GPU Gems 3 is out, and it contains a chapter on real-time 3D simulation & rendering of fluids (smoke and liquids) on the GPU, and is available as a free sample chapter online. You may have seen some of these results before on Keenan Crane’s website.

GPU Gems 3