Neighborhood grid: A novel data structure for fluids animation with GPU computing

Highlights

• We present a new data structure for the neighborhood gathering on fluid simulation, called neighborhood grid.

• The neighborhood grid has an expressive speedup against the uniform grid on GPUs.

• The neighborhood grid uses less memory when compared with the uniform grid.

Abstract

This paper introduces a novel and efficient data structure, called neighborhood grid, capable of supporting large number of particle based elements on GPUs (graphics processing units), and is used for optimizing fluid animation with the use of GPU computing. The presented fluid simulation approach is based on SPH (smoothed particle hydrodynamics) and uses a unique algorithm for the neighborhood gathering. The brute force approach to neighborhood gathering of $n$ particles has complexity $O\left(n^2\right)$, since it involves proximity queries of all pairs of fluid particles in order to compute the relevant mutual interactions. Usually, the algorithm is optimized by using spatial data structures which subdivide the environment in cells and then classify the particles among the cells based on their position, which is not efficient when a large number of particles are grouped in the same cell. Instead of using such approach, this work presents a novel and efficient data structure that maintains the particles into another form of proximity data structure, called neighborhood grid. In this structure, each cell contains only one particle and does not directly represent a discrete spatial subdivision. The neighborhood grid does process an approximate spatial neighborhood of the particles, yielding promising results for real time fluid animation, with results that goes up to 9 times speedup, when compared to traditional GPU approaches, and up to 100 times when compared against CPU implementations.

Introduction

Realism in real-time graphical simulations includes the search for real behaviors and physics. Due to the graphics technology improvements, simulation of natural phenomena, such as water flows or smoke, has become possible to be performed in real time and interactive environments, like scientific applications and digital games. In fact, this kind of simulation is now quite popular in computer games, digital movies and animations. It is important to state that in real-time simulations, there is a trade-off between realism and interactivity, and most of the times the realistic behavior is put aside in order to have interactive frame rates.

Many non-graphics algorithms traditionally executed on the CPU are often suitable for parallel execution, which makes them appropriate to be implemented on GPUs (graphics processing units). Fluid animation that explores this programming model on the GPU is a promising line of research, since it can drastically speedup the computation cost of the fluids’ behavior  [4]. This work presents a new data structure for speeding up the neighborhood gathering which can be applied in fluid simulation. The concepts of the proposed architecture could also be applied to other multi-core processors like multi-core CPUs, the Playstation 4, Xbox One, and clusters.

GPUs are a collection of SIMD (single instruction, multiple data) processors designed to run a streamed graphics pipeline. It is a computational model where the processing of each pixel is independent of the others and usually requires localized memory reads (texture fetching). There are rules of thumb to create efficient streamed applications, where the most important one is to organize the data streams in order to maximize memory read performance based on locality. These rules tend to result in a more efficient usage of available cache memory and read ahead mechanisms of these devices. The proposed simulation system makes use of such strategies.

The SPH (smoothed particle hydrodynamics) method simulates the fluid as a set of discrete elements, referred as particles. In order to process the interaction between the particles using the Lagrangian approach, a neighborhood-gathering algorithm is needed in order to process the forces among the particles. The naive approach of such algorithm has complexity of $O\left(n^2\right)$, since it has to process each particle against all the other $n-1$ particles. Most of the research on parallel and distributed SPH fluid simulation tries to avoid the high complexity of proximity queries by applying some form of spatial subdivision to the environment and by classifying particles among the cells based on their position. To accelerate data fetching in a parallel hardware (such as GPUs) the particles listed must be sorted in a way that all particles on the same cells are grouped together. This approach helps decrease the number of proximity queries, but it is very sensible to the maximum number of particles that can fit in a single cell. In this work, instead of using a similar approach, it is proposed a novel data structure which maintains particles into another kind of proximity based data structure. In this data structure, called neighborhood grid, each cell stores only one particle and does not directly represent a discrete spatial subdivision. The neighborhood grid is an approximated representation of the system of neighbors of the environment that maps the $N$-dimensional environment to a discrete map (lattice) with $N$ dimensions. Hence, particles that are close in a neighborhood sense appear close to each other in the map. Another approach is to think of it as a multi-dimensional compression of the simulated environment that still stores the original position information of all particles.

Contributions: This work presents a novel parallel data structure for graphical real-time fluid animation based on the SPH method. This solution uses a novel data structure, called neighborhood grid, in order to gather the neighborhoods of the particles in an optimized manner. By doing so, this proposal fills the lack of GPU bounded architectures that usually process all elements in the scene at each frame, thus being an efficient solution for other parallel and distributed solutions of fluid simulations.

Paper summary: This work is organized as follows. After referring to the SPH method in Section  2 and the related works of fluid simulation in Section  3, the neighborhood grid data structure is introduced in Section  4. In Section  5 the architecture environment on GPUs and the acceleration data structures employed in the simulations are described. In Section  6 some results are shown and, in Section  7, the conclusions are presented.