Liquid simulation on lattice-based tetrahedral meshes
James O'Brien2007, ACM SIGGRAPH 2007 computer animation festival
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
We describe a method for animating incompressible liquids with detailed free surfaces. For each time step, semi-Lagrangian contouring computes a new fluid boundary (represented as a fine surface triangulation) from the previous time step's fluid boundary and velocity field. Then a mesh generation algorithm called isosurface stuffing discretizes the region enclosed by the new fluid boundary, creating a tetrahedral mesh that grades from a fine resolution at the surface to a coarser resolution in the interior. The mesh has a structure, based on the body centered cubic lattice, that accommodates graded tetrahedron sizes but is regular enough to aid efficient point location and to save memory used to store geometric properties of identical tetrahedra. Although the mesh is warped to conform to the liquid boundary, it has a mathematical guarantee on tetrahedron quality, and is generated very rapidly. Each successive time step entails creating a new triangulated liquid surface and a new tetrahedral mesh. Semi-Lagrangian advection computes velocities at the current time step on the new mesh. We use a finite volume discretization to perform pressure projection required to enforce the fluid's incompressibility, and we solve the linear system with algebraic multigrid. A novel thickening scheme prevents thin sheets and droplets of liquid from vanishing when their thicknesses drop below the mesh resolution. Examples demonstrate that the method captures complex liquid motions and fine details on the free surfaces without suffering from excessive volume loss or artificial damping.
Related papers
Optimization-based fluid simulation on unstructured meshes
2010
We present a novel approach to fluid simulation, allowing us to take into account the surface energy in a precise manner. This new approach combines a novel, topology-adaptive approach to deformable interface tracking, called the deformable simplicial complexes method (DSC) with an optimization-based, linear finite element method for solving the incompressible Euler equations. The deformable simplicial complexes track the surface of the fluid: the fluid-air interface is represented explicitly as a piecewise linear surface which is a subset of tetrahedralization of the space, such that the interface can be also represented implicitly as a set of faces separating tetrahedra marked as inside from the ones marked as outside. This representation introduces insignificant and controllable numerical diffusion, allows robust topological adaptivity and provides both a volumetric finite element mesh for solving the fluid dynamics equations as well as direct access to the interface geometry data, making inclusion of a new surface energy term feasible. Furthermore, using an unstructured mesh makes it straightforward to handle curved solid boundaries and gives us a possibility to explore several fluid-solid interaction scenarios.
IEEE TVCG 1 Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes
2014
Abstract—In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We charact...
Simulating Liquids and Solid-Liquid Interactions with Lagrangian Meshes
This paper describes a Lagrangian finite element method that simulates the behavior of liquids and solids in a unified framework. Local mesh improvement operations maintain a high-quality tetrahedral discretization even as the mesh is advected by fluid flow. We conserve volume and momentum, locally and globally, by assigning each element an independent rest volume and adjusting it to correct for deviations during remeshing and collisions. Incompressibility is enforced with per-node pressure values, and extra degrees of freedom are selectively inserted to prevent pressure locking. Topological changes in the domain are explicitly treated with local mesh splitting and merging. Our method models surface tension with an implicit formulation based on surface energies computed on the boundary of the volume mesh. With this method we can model elastic, plastic, and liquid materials in a single mesh, with no need for explicit coupling. We also model heat diffusion and thermoelastic effects, which allow us to simulate phase changes. We demonstrate these capabilities in several fluid simulations at scales from millimeters to meters, including simulations of melting caused by external or thermoelastic heating.
Fluid animation with dynamic meshes
ACM Transactions on Graphics, 2006
: Top: A paddle mixes smoke in a tank. Bottom: A cross-section of the simulation meshes used for each frame.
Practical animation of liquids
Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01, 2001
We present a general method for modeling and animating liquids. The system is specifically designed for computer animation and handles viscous liquids as they move in a 3D environment and interact with graphics primitives such as parametric curves and moving polygons. We combine an appropriately modified semi-Lagrangian method with a new approach to calculating fluid flow around objects. This allows us to efficiently solve the equations of motion for a liquid while retaining enough detail to obtain realistic looking behavior. The object interaction mechanism is extended to provide control over the liquid's 3D motion. A high quality surface is obtained from the resulting velocity field using a novel adaptive technique for evolving an implicit surface.
A Multigrid Framework for Real-Time Simulation of Deformable Volumes
2005
In this paper, we present a multigrid framework for constructing implicit, yet interactive solvers for the governing equations of motion of deformable volumetric bodies. We have integrated linearized, corotational linearized and non-linear Green strain into this framework. Based on a 3D finite element hierarchy, this approach enables realistic simulation of objects exhibiting an elastic modulus with a dynamic range of several orders of magnitude. Using the linearized strain measure, we can simulate 50 thousand tetrahedral elements with 20 fps on a single processor CPU. By using corotational linearized and non-linear Green strain, we can still simulate five thousand and two thousand elements, respectively, at the same rates.
Visual Simulation of Multiple Fluids in Computer Graphics: A State-of-the-Art Report
Journal of Computer Science and Technology, 2018
Realistic animation of various interactions between multiple fluids, possibly undergoing phase change, is a challenging task in computer graphics. The visual scope of multi-phase multi-fluid phenomena covers complex tangled surface structures and rich color variations, which can greatly enhance visual effect in graphics applications. Describing such phenomena requires more complex models to handle challenges involving calculation of interactions, dynamics and spatial distribution of multiple phases, which are often involved and hard to obtain real-time performance. Recently, a diverse set of algorithms have been introduced to implement the complex multi-fluid phenomena based on the governing physical laws and novel discretization methods to accelerate the overall computation while ensuring numerical stability. By sorting through the target phenomena of recent research in the broad subject of multiple fluid, this state-of-the-art report summarizes recent advances on multi-fluid simulation in computer graphics.
Animation of Gas-Liquid Systems Through Lattice Gas Cellular Automata and Smoothed Particle Hydrodynamics
The past two decades showed a rapid growing of physically-based modeling of fluids for computer graphics applications. Techniques in the field of Computational Fluid Dynamics (CFD) have been applied for realistic fluid animation for virtual surgery simulators, computer games and visual effects.
Fast fluid simulation using residual distribution schemes
Eurographics Workshop on Natural Phenomena, 2007
We present a fast method for physically-based animation of fluids on adaptive, unstructured meshes. Our algorithm is capable of correctly handling large-scale fluid forces, as well as their interaction with elastic objects. Our adaptive mesh representation can resolve boundary conditions accurately while maintaining a high level of efficiency. Categories and Subject Descriptors (according to ACM CCS): I. 3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling; I. 3.6 [ ...
Real-time interactive animations of liquid surfaces with Lattice-Boltzmann engines
Australian Journal of Basic and Applied Sciences
A physics-based graphic engine supporting interactive animations of free water surfaces at real-time is presented. The algorithm is based on a lattice-Boltzmann model of the shallow waters equations and the interaction between the surface and external objects is achieved by means of source terms. The engine is capable of produce scenes of ponds whose surface reacts to perturbations introduced by the user or controlled by the computer, like drizzle or the stirring of a finger.
Related papers
Realistic Animation of Liquids
Graphical Models and Image Processing, 1996
We present a comprehensive methodology for realistically animating liquid phenomena. Our approach unifies existing computer graphics techniques for simulating fluids and extends them by incorporating more complex behavior. It is based on the Navier-Stokes equations which couple momentum and mass conservation to completely describe fluid motion. Our starting point is an environment containing an arbitrary distribution of fluid, and submerged or semi-submerged obstacles. Velocity and pressure are defined everywhere within this environment, and updated using a set of finite difference expressions. The resulting vector and scalar fields are used to drive a height field equation representing the liquid surface. The nature of the coupling between obstacles in the environment and free variables allows for the simulation of a wide range of effects that were not possible with previous computer-graphics fluid models. Wave effects such as reflection, refraction and diffraction, as well as rotational effects such as eddies, vorticity, and splashing are a natural consequence of solving the system. In addition, the Lagrange equations of motion are used to place buoyant dynamic objects into a scene, and track the position of spray and foam during the animation process. Typical disadvantages to dynamic simulations such as poor scalability and lack of control are addressed by assuming that stationary obstacles align with grid cells during the finite difference discretization, and by appending terms to the Navier-Stokes equations to include forcing functions. Free surfaces in our system are represented as either a collection of massless particles in 2D, or a height field which is suitable for many of the water rendering algorithms presented by researchers in recent years.
A Semi-Lagrangian Contouring Method for Fluid Simulation
In this article, we present a semi-Lagrangian surface tracking method for use with fluid simulations. Our method maintains an explicit polygonal mesh that defines the surface, and an octree data structure that provides both a spatial index for the mesh and a means for efficiently approximating the signed distance to the surface. At each timestep, a new surface is constructed by extracting the zero set of an advected signed-distance function. Semi-Lagrangian backward path tracing is used to advect the signed-distance function. One of the primary advantages of this formulation is that it enables tracking of surface characteristics, such as color or texture coordinates, at negligible additional cost. We include several examples demonstrating that the method can be effectively used as part of a fluid simulation to animate complex and interesting fluid behaviors.
A Unified Lagrangian Approach to Solid-Fluid Animation
2005
We present a framework for physics-based animation of deforming solids and fluids. By merging the equations of solid mechanics with the Navier-Stokes equations using a particle-based Lagrangian approach, we are able to employ a unified method to animate both solids and fluids as well as phase transitions. Central to our framework is a hybrid implicit-explicit surface generation approach which is capable of representing fine surface detail as well as handling topological changes in interactive time for moderately complex objects. The generated surface is represented by oriented point samples which adapt to the new position of the particles by minimizing the potential energy of the surface subject to geometric constraints. We illustrate our algorithm on a variety of examples ranging from stiff elastic and plasto-elastic materials to fluids with variable viscosity.
GPU Based Fluid Animation over Elastic Surface Models
2009
In this work, we focus on flow animation in elastic surfaces described by mass-spring models for computer game applications. We propose the combination of an efficient fluid model, that does not require solution of complicated equations, with a mass-spring approach to simulate the deformable surface. Firstly, we describe the fluid model for simulating the flow and its GPU implementation. The simulation method is based on a particle system, that evolves over a lattice. This lattice is defined over the surface domain. A set of local rules determine the interaction between particles. The elastic surface is simulated by a GPU based mass-spring system, geometrically represented by a regular mesh. The fluid particles are guided by the surface topography interacting with the elastic mesh due to external, elastic and damping forces. In the experimental results we emphasize the fact that physically plausible flow/deformation phenomena can be efficiently reproduced and animated in real time by the combined technique.
Animating Gases with Hybrid Meshes
This paper presents a method for animating gases on unstructured tetrahedral meshes to efficiently model the interaction of fluids with irregularly shaped obstacles. Because our discretization scheme parallels that of the standard staggered grid mesh, we are able to combine tetrahedral cells with regular hexahedral cells in a single mesh. This hybrid mesh offers both accuracy near obstacles and efficiency in open regions.
Physics-based Surface Modeling using Quasi-Static Liquids
Computer-Aided Design and Applications, 2009
This paper presents a physics-based modeling approach for the creation of high quality surfaces for application in CAGD. Physics-based modeling is commonly used in animation and scientific modeling, and simulates realistic dynamic motion for computer graphics. We propose a physics-based modeling of liquid surface motion as a means to generate complex geometry. Regions of a model are defined to be in a solid phase and other parts are in a liquid phase. The liquid surface is mobile and moves in response to physics-based forces resulting in a smooth, minimum energy surface. The objects created by this method are referred to as Temporal Computational Objects (TCO's) and provide a capability that is fully integrated with standard CAD, FEA and CAM utilities. We demonstrate the usefulness of the approach with a wide range of examples that produce high quality physics-based surface models that have been analyzed and fabricated.
Lattice Gas Cellular Automata for Computational Fluid Animation
Computing Research Repository, 2005
The past two decades showed a rapid growing of physically-based modeling of fluids for computer graphics applications. In this area, a common top down approach is to model the fluid dynamics by Navier-Stokes equations and apply a numerical techniques such as Finite Differences or Finite Elements for the simulation. In this paper we focus on fluid modeling through Lattice Gas Cellular Automata (LGCA) for computer graphics applications.
Particle-based fluid simulation for interactive applications
2003
Realistically animated fluids can add substantial realism to interactive applications such as virtual surgery simulators or computer games. In this paper we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. The method is an extension of the SPH-based technique by Desbrun to animate highly deformable bodies. We gear the method towards fluid simulation by deriving the force density fields directly from the Navier-Stokes equation and by adding a term to model surface tension effects. In contrast to Eulerian grid-based approaches, the particle-based approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation. In addition, the particles can directly be used to render the surface of the fluid. We propose methods to track and visualize the free surface using point splatting and marching cubes-based surface reconstruction. Our animation method is fast enough to be used in interactive systems and to allow for user interaction with models consisting of up to 5000 particles.
Interactive free surface fluids with the lattice Boltzmann method
2005
In this paper we present our algorithm for animating fluids with a free surface. It is based on the Lattice-Boltzmann Method, instead of a direct discretization of the Navier-Stokes equations. This allows a relatively simple treatment of the free surface boundary conditions at high computational efficiency, without sacrificing the underlying physics. We give a detailed description of our algorithm, focussing on details that are required to achieve a good visual appearance. Furthermore we describe how to implement our adaptive time stepping technique to achieve flexible and stable simulations. We will demonstrate the speed and capabilities of the method with animations from different interactive test cases. These run with, on average, more than 20 frames per second on a standard desktop PC.
Simulating Fluid-Solid Interaction
Graphics Interface, 2003
Though realistic eulerian fluid simulation systems now provide believable movements, straightforward render- able surface representation, and affordable computation costs, they are still unable to deal with non-static objects in a realistic manner. Namely, objects can not have an influence on the fluid and be simultaneously affected by the fluid's motion. In this paper, a simulation scheme for fluids allowing automatic
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.