Lattice Boltzmann Liquid Simulation with Moving Objects on Graphics Hardware

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1 Lattice Boltzmann Liquid Simulation with Moving Objects on Graphics Hardware Duncan Clough Supervised by: James Gain, Michelle Kuttel 1 Introduction Fluid simulation is a common element in recent feature films. These effects include water rushing into a sinking ship in Poseidon, whirlpools in the ocean in Pirates of the Caribbean 3, and a fiery skeleton in Ghost Rider. Simulating fluids requires massive computation in order to reach the levels of realism audiences now expect. This time is not always available for simulation, as computers are often used in a visual effects setting for compositing and rendering high quality scenes. Scenes with fluids also undergo iterative development, requiring multiple simulation runs during their production. An inexpensive means of increasing simulation speed will provide animators with more time to choose the prefect parameters for a fluid within a scene, ultimately resulting in higher quality visual effects.. In recent years Graphics Processing Units (GPUs) have shown, through their multithreaded multi-processor architecture, that they have great potential to speed up problems that require large amounts of computation. GPUs have been specifically designed to quickly and efficiently process mathematical operations commonly used in rendering. This specialisation allows GPUs to offer faster computation than a Central Processing Unit (CPU) for certain operations, because the GPU does not have to be able to do the general housekeeping operations. Since GPU development and supply is driven by the lucrative gaming industry, GPUs have also become a relatively cheap source of computational power. We plan to follow on from the work done by Reid et al. [16], who successfully developed and tested a parallel implementation of the dclough@cs.uct.ac.za jgain@cs.uct.ac.za mkuttel@cs.uct.ac.za Lattice Boltzmann Method (LBM) using MPI that could simulate liquids with a free surface in scenes that included static objects (a free surface is defined to be the boundary between two homogeneous fluids in this case, the visible boundary between the liquid and its surrounding gas). This research project will focus on investigating the performance benefits achievable through implementing the LBM on a GPU using NVIDIA s CUDA. We will also further extend the LBM simulation to include moving objects. We also intend to develop a GPU LBM Houdini Fluid Dynamics plug-in. Houdini is a 3D animation and visual effects software package developed by Side Effects Software Inc. that is popular in the visual effects and animation industry. Houdini provides a procedural framework for building and rendering scenes, as well as an interface for developing custom plug-ins that can be included in scenes. Through this plug-in we will be able to take advantage of Houdini s advanced rendering capabilities. 2 Related Work 2.1 Fluid Simulation There are two aspects to fluid simulation generation of the fluid dynamics and subsequent approximation of the fluid s surface. Almost all fluid simulation methods can be categorised as either Eulerian, Lagrangian or Semi-Lagrangian [1]. Lagrangian methods use a particle system, in which particles move freely and interact with each other; the behaviour of the particles defines the motion of the fluid. The Eulerian approach focuses on modelling the flow of a fluid through a fixed grid, and modelling how interactions occur on 1

2 that grid. In this case, the interactions on the grid define the motion of the fluid. Semi- Lagrangian methods are usually Eulerian in nature, but incorporate various aspects of the Lagrangian approach. The grid-based Eulerian methods are often best suited to parallel architectures because of their static grid structure. The Lattice-Boltzmann Method (LBM), is a popular grid-based approach to simulating fluid flows, especially on high-performance parallel platforms, such as clusters and GPUs. The LBM provides a discrete approximation of the Navier-Stokes equations the equations that describe fluid dynamics. Approximations of fluid particles are moved around a lattice according to probability distribution functions that provide a mesoscopic estimate of the particle interaction within a fluid. The LBM is linear with respect to time: each timestep depends only on the previous time step. This linearity, combined with its cellular grid structure, makes the algorithm easy to implement on parallel architectures [16]. In order to visually represent this field as a liquid, the surface of the liquid needs to be extracted from the vector field. This is traditionally done using the Marching Cubes algorithm [10]. This provides a good approximate fluid surface, but refinements are required to make interaction between the free surface and other objects visually appealing [17]. 2.2 Moving Objects The addition of moving objects can be divided into two components: modelling the interactions between objects and fluid, and modelling the physics of object movement. Full two-way coupled fluid simulations (when both objectto-fluid and fluid-to-object momentum transfer occur), require an additional physics engine to manage object movement [2]. Scripted object movement can be used [8] instead of a physics engine with the added benefit of less computation and complexity. Fluid interaction with deformable objects is beyond the scope of this project. Thürey et al. [17] present a full two-way coupled LB fluid simulation. Object-to-fluid momentum transfer is done by adding momentum terms, to the object boundary calculations, where object momentum is calculated using Newton s second law. Fluid-to-object momentum transfer is less trivial, requiring an approximation of the force applied to an object based on distribution functions in contact with the object s surface [7]. Li et al. [8] implement a fluid solver on a GPU that included one-way object-to-fluid coupling for fluids without a free surface. This implementation was based on work down by Mei et al. [12, 13] and is a slightly different method to that used by Thürey et al. [17]. Further investigation would be required to deduce which method is best suited for GPU computation. 2.3 GPU Implementations of the LBM In 2001 the first programmable GPUs were commercially released, and soon thereafter, GPUs were applied to general purpose computing instead of the usual real-time implementations of rendering effects [11]. In 2003, Li et al. [9] published experimental results of their GPU implementation of the LBM, which showed a possible speed-up of 50 for simulating the behaviour of smoke. This work was subsequently extended to include computation on a cluster of GPUs [5], simulations with moving objects [8, 19], and embedded grid structures that allow an increase of simulation resolution to follow more complex scene features [20]. This work does not include the generation of a liquid s free surface and was done using older GPUs and NVIDIA s Cg language which is designed for implementing custom graphics effects on the GPU [6] and not general purpose computation. Their latest work reports a speed-up of Their optimisations of the GPU implementation mainly deal with managing textures and tweaking implementation details and are thus better suited to Cg s pipeline. These adaptions are now less relevant since we are able to use tools such as CUDA that are better suited for general purpose computation, like the LBM. Peng et al. [15] tested the parallel implementation of the LBM on a cell processor cluster built from PlayStation 3 consoles, and a GPU implementation using CUDA. Their 2

3 work reports a speed-up of 8.76 for the GPU, however, no specific optimisations to the LBM in CUDA are reported. It is expected that this result can easily be improved upon by taking into account memory usage, thread management and processor occupancy, all of which can lead to significant performance gains [3]. To the best of our knowledge, LBM simulations of liquids with a free surface interacting with moving objects has yet to be implemented on the GPU using CUDA. 3 Research Questions This research will focus on implementation of the LBM on a GPU. We are interested in looking at the performance improvements and any visual differences between the CPU and GPU implementations that may arise. The following four questions will provide focus for this research project. Compared to a single CPU implementation, what speed-up and run-time improvements can be achieved by implementing the LBM on a GPU? This is the most important question of the research project. It is the primary identifier of how viable and successful a GPU implementation would be in the visual effects industry. To answer this question, we will need to develop GPU and CPU implementations of the LBM. We will then compare the simulation run-time for each implementation (details of to be discussed in Section 5.1). Based on the results from other researchers (discussed in Section 2.3) we aim to achieve a speed-up of at least 25. Furthermore, this comparison will be done with different scenes to identify which scenetypes are best suited for each implementation. Different scenes can be creating by manipulating various scene attributes such as obstacle complexity, scene symmetry, similarity of initial and rest positions and amount/velocity of liquid flow. What are the limitations or constraints associated with implementing the LBM on a GPU? The architecture of a GPU is very different to that of a CPU, therefore various modifications to the general LBM algorithm will be made in order to maximise performance gains [18]. These limitations and constraints will be critical to understanding parts of the LBM that will need special focus in order to improve the practical use of this method on a GPU. Available memory during the simulation is expected to limit the size of scenes. We will investigate what these limits are and, given time, suggest possible modifications to reduce the effects of this limitation. Are there any reductions in visual quality necessary in order to achieve an efficient GPU LBM implementation? As already discussed, various changes may be required in order implement the LBM on a GPU. It is possible that these changes could affect the visual quality of an LBM simulation. Since visual quality is the most important aspect of visual effects, identifying and providing solutions to these differences is extremely important. 4 Research Outcomes We expect to develop two fully functional LBM simulation systems: one on a CPU and the other on a GPU. These systems are expected to be able to visually model the flow of liquids and their interaction with moving objects within a scene. Using these systems we intend to identify the possible performance benefits that can be obtained by implementing an LB simulation on a GPU. Modifications to the standard LBM algorithm made to increase the efficiency of the GPU implementation will also be investigated. It is expected that the output of the LBM simulation will appear to be visually similar to real liquid. This is an important result for the performance results to be meaningful in the visual effects industry. A Houdini plug-in for the simulation will also be developed. This will simplify the rendering process, and test the practicality of the system within a standard visual effects software package. 3

4 5 Research Approach Development of a working simulation system is vital for the success of this project. We will, therefore, discuss the planning behind implementing this system. Once the system is developed, we will run performance tests on the CPU and GPU using Houdini to render the results. Table 1 provides a proposed overview of deadlines for this research project. Figure 1 at the end of this document shows the time allocations for the proposed work. 5.1 System Development There are five major components that need to be developed for this project. Single CPU LBM Implementation: This will provide results with which to compare the GPU implementation. The relative simplicity of a single CPU implementation will also act as a prototype with which possible extensions can be explored before implementing them on a GPU architecture. Liquid Surface Extraction: Since the focus of this research is on producing visually appealing results, the extraction of the free surface is an integral part of the simulation. We intend to use the standard approach to this problem, the Marching Cubes algorithm. The LBM outputs a vector field representing the fluid flow for the simulation domain. Marching Cubes divides this domain into cubes and identifies the cubes positioned at the boundaries of the liquid. For each of these cubes, the algorithm approximates a polygon (from a set of predefined possible configurations) to fit the cube, based on information from surrounding cubes and the vector field produced by the LBM. Minor extensions to Marching Cubes will be needed to improve the boundaries between objects and the free surface. GPU LBM Implementation: The LBM will be extended to a GPU architecture to reduce simulation run-time. We intend to make use of NVIDIA s CUDA [14] to implement the LBM. Moving Obstacle Integration: Our implementation will be developed to include fluid interaction with moving objects. For this project, moving objects refers to objects with a static shape that can move within a scene and interact with any fluid with which they come into contact. This is a two way interaction with a transfer of momentum from the object to the fluid as well as from the fluid to the object. Interaction between objects will be considered a possible extension to the project, given sufficient time. For our purposes, visual realism will be of greater importance than physical accuracy. This will allow us to use methods to reduce computation time at the cost of physical accuracy, such as using a multi-resolution lattice [20]. The speeds at which objects can move will be limited by the granularity of the simulation lattice and time-step. This is a relatively small constraint as both the time-step and the lattice granularity can be adjusted to accommodate a wide range of speeds. Houdini Fluid Solver Plug-in: We intend to develop a plug-in that will be an interface between our LBM simulations and Houdini. The benefit of building this plug-in is that we will not have to build a custom renderer, but can instead make use of Houdini s powerful Mantra renderer. This will also allow us to take advantage of Houdini s effective liquid rendering capabilities, ultimately yielding superior visuals. 6 Testing 6.1 Performance Testing The performance of both the CPU implementation and the GPU implementation will be measured in a series of test simulations. The focus of these tests is to identify the speed-up and reductions in run-time achievable with a GPU implementation. It is anticipated that developing and running these simulations will take up a significant part of the research time. This time has been taken into account for the work schedule presented in Figure 1. 4

5 Date Task 2009 June 2D LBM CPU Prototype 2009 July 2D LBM CPU Prototype with Moving Obstacles 2009 July GPU Implementation Design Iteration August GPU Implementation Design Iteration August 2D CPU LBM Implementation with Surface Extraction September 3D CPU LBM Implementation with Moving Obstacles 2009 October Houdini Integration Complete 2009 October 2D GPU Implementation with Moving Obstacles Complete 2009 November GPU Implementation Design Iteration December 3D GPU Implementation with Moving Obstacles Working 2010 April GPU Implementation Finalised 2010 May Testing Complete 2010 September Write-up Complete Table 1: Key Deadlines for Project Each test case will have a scene specifically designed to test a certain aspect of the simulation. For example, flooding a large city with water could be used to test the effect of many objects on performance. A common test case involving a wall of water collapsing from one side of the domain to the other, helps identify how scene asymmetry affects performance. We will choose a selection of test cases that are the most appropriate to our investigations. 6.2 Simulation Validation In the visual effects industry, visual quality is of more importance than physical accuracy. Furthermore, maintaining physical accuracy would result in simulation constraints reducing the possible benefits to be gained from a GPU implementation. It would also require further tests that would increase the scope of this project. Extensive physical validation of simulations will, therefore, not be considered vital to the success of this research. Simple physical validation will be done by comparing standard analytical solutions [4] with simulation results. The focus will be on the visual accuracy of the simulation. If the simulation results in liquid flows that are visually realistic, then our results will be acceptable for use in the visual effects industry. This validation will be done in the form of user tests, which will focus on specific aspects of visual accuracy and realism as well as the overall appeal. Breaking down visual accuracy and realism into separate components will help identify specific strengths and weaknesses of the simulation. References [1] Bridson, R., Fedkiw, R., and Müller-Fischer. Fluid simulation. In SIGGRAPH 06: SIGGRAPH Course Notes (2006). [2] Carlson, M., Mucha, P. J., and Turk, G. Rigid fluid: animating the interplay between rigid bodies and fluid. 5

6 ACM Trans. Graph. 23, 3 (2004), [3] Che, S., Meng, J., and Sheaffer, J. W. A performance study of general purpose applications on graphics processors. In First Workshop on General Purpose Processing on Graphics Processing Units (2007). [4] Chen, S., and Doolen, G. D. Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics 30 (January 1998), [5] Fan, Z., Qiu, F., Kaufman, A., and Yoakum-Stover, S. GPU cluster for high performance computing. In SC 04: Proceedings of the 2004 ACM/IEEE conference on Supercomputing (Washington, DC, USA, 2004), IEEE Computer Society, p. 47. [6] Fernando, R., and Kilgard, M. J. The Cg Tutorial: The Definitive Guide to Programmable Real-Time Graphics. Addison-Wesley Longman Publishing Co., Inc., Boston, MA, USA, [7] Ladd, A. J. C. Numerical simulations of particulate suspensions via a discretized boltzmann equation. part 2. numerical results. Journal of Fluid Mechanics Digital Archive 271, -1 (1994), [8] Li, W., Fan, Z., Wei, X., and Kaufman, A. GPU-based flow simluation with complex boundaries. In CPU Gems 2, M. Pharr, Ed. Addison Wesley, March 2005, ch. 47, pp [9] Li, W., Wei, X., and Kaufman, A. Implementing Lattice Boltzmann computation on graphics hardware. The Visual Computer 19, 7 8 (December 2003), [10] Lorensen, W. E., and Cline, H. E. Marching cubes: A high resolution 3d surface construction algorithm. In SIG- GRAPH 87: Proceedings of the 14th annual conference on Computer graphics and interactive techniques (New York, NY, USA, 1987), ACM, pp [11] Macedonia, M. The gpu enters computing s mainstream. Computer 36, 10 (October 2003), [12] Mei, R., Li-Luo, S., and Shyy, W. An accurate curved boundary treatment in the lattice boltzmann method. Tech. rep., [13] Mei, R., Shyy, W., Yu, D., and Luo, L.-S. Lattice Boltzmann method for 3-d flows with curved boundary. J. Comput. Phys. 161, 2 (2000), [14] NVIDIA. CUDA zone. nvidia.com/object/cuda_home.html, [15] Peng, L., Nomura, K.-i., Oyakawa, T., Kalia, R. K., Nakano, A., and Vashishta, P. Parallel Lattice Boltzmann flow simulation on emerging multi-core platforms. In Euro-Par 2009 Parallel Processing, vol. 5168/2008 of Lecture Notes in Computer Science. Springer Berlin / Heidelberg, August 2008, pp [16] Reid, A. Parallel fluid dynamics for the animation industry. Master s thesis, University of Cape Town, Cape Town, South Africa, May [17] Thürey, N., Iglberger, K., and Rüde, U. Free surface flows with moving and deforming objects for LBM. In Vision, Modeling, and Visualization (2006). [18] Tölke, J. Implementation of a Lattice Boltzmann kernel using the compute unified device architecture developed by NVIDIA. Computing and Visualization in Science (July 2008). [19] Wei, X., Li, W., Mueller, K., and Kaufman, A. The lattice-boltzmann method for simulating gaseous phenomena. Visualization and Computer Graphics, IEEE Transactions on 10, 2 (March- April 2004), [20] Zhao, Y., Qiu, F., Fan, Z., and Kaufman, A. Flow simulation with locally-refined LBM. In I3D 07: Proceedings of the 2007 symposium on Interactive 3D graphics and games (New York, NY, USA, 2007), ACM, pp

7 7 ID Task Name 1 Implementation 2 CPU Implementation 3 2D Prototype 4 2D with Moving Obstacles 5 2D with Surface Extraction 6 3D Full Simulation 7 CPU Implementation Complete 8 GPU Implementation 9 GPU Design Iteration 1 10 GPU Design Iteration 2 11 GPU Design Iteration D GPU LBM with Moving Obstacles 13 3D GPU LBM with Moving Obstacles 14 GPU Implementation Complete 15 Houdini Integration 16 Testing 17 Writing Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep 09/25 04/18 Lattice Boltzmann Liquid Simulation with Moving Objects on Graphics Hardware Task Split Progress Milestone Summary Project Summary External Tasks External Milestone Deadline Figure 1: A Gantt chart outlining the proposed work plan.

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