Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [ GM97] have been addressed, thereby making these models interesting and useful for both offline and real-time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass-spring systems, meshfree methods, coupled particle systems and reduced deformable models based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.

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Physically Based Deformable Models in Computer Graphics

Physically Based Deformable Models in Computer Graphics.

We present a weakly compressible form of the Smoothed Particle Hydrodynamics method (SPH) for fluid flow based on the Tait equation. In contrast to commonly employed projection approaches that strictly enforce incompressibility, time-consuming solvers for the Poisson equation are avoided by allowing for small, user-defined density fluctuations. We also discuss an improved surface tension model that is particularly appropriate for single-phase free-surface flows. The proposed model is compared to existing models and experiments illustrate the accuracy of the approach for free surface flows. Combining the proposed methods, volume-preserving low-viscosity liquids can be efficiently simulated using SPH. The approach is appropriate for medium-scale and small-scale phenomena. Effects such as splashing and breaking waves are naturally handled.

Weakly compressible SPH for free surface flows

We present a unified dynamics framework for real-time visual effects. Using particles connected by constraints as our fundamental building block allows us to treat contact and collisions in a unified manner, and we show how this representation is flexible enough to model gases, liquids, deformable solids, rigid bodies and cloth with two-way interactions. We address some common problems with traditional particle-based methods and describe a parallel constraint solver based on position-based dynamics that is efficient enough for real-time applications.

Unified particle physics for real-time applications

In this paper, we present a method for simulating the interaction of fluids with deformable solids. The method is designed for the use in interactive systems such as virtual surgery simulators where the real-time interplay of liquids and surrounding tissue is important. In computer graphics, a variety of techniques have been proposed to model liquids and deformable objects at interactive rates. As important as the plausible animation of these substances is the fast and stable modeling of their interaction. The method we describe in this paper models the exchange of momentum between Lagrangian particle-based fluid models and solids represented by polygonal meshes. To model the solid-fluid interaction we use virtual boundary particles. They are placed on the surface of the solid objects according to Gaussian quadrature rules allowing the computation of smooth interaction potentials that yield stable simulations. We demonstrate our approach in an interactive simulation environment for fluids and deformable solids. Copyright © 2004 John Wiley & Sons, Ltd.

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Interaction of fluids with deformable solids

In this paper, we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate blood as a fluid with free surfaces. While SPH was originally designed to simulate astronomical objects, 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. Our method can be used in interactive surgical training systems with models of up to 3000 particles.

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Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics

We present a new method for enhancing shallow water simulations by the effect of overturning waves. While full 3D fluid simulations can capture the process of wave breaking, this is beyond the capabilities of a pure height field model. 3D simulations, however, are still too expensive for real-time applications, especially when large bodies of water need to be simulated. The extension we propose overcomes this problem and makes it possible to simulate scenes such as waves near a beach, and surf riding characters in real-time. In a first step, steep wave fronts in the height field are detected and marked by line segments. These segments then spawn sheets of fluid represented by connected particles. When the sheets impinge on the water surface, they are absorbed and result in the creation of particles representing drops and foam. To enable interesting applications, we furthermore present a two-way coupling of rigid bodies with the fluid simulation. The capabilities and efficiency of the method will be demonstrated with several scenes, which run in real-time on today's commodity hardware.

Real-time Breaking Waves for Shallow Water Simulations

Disclosed is a method of generating a three-dimensional (3D) surface defined by a boundary of a 3D point cloud. The method comprises generating density and depth maps from the 3D point cloud, constructing a 2D mesh from the depth and density maps, transforming the 2D mesh into a 3D mesh, and rendering 3D polygons defined by the 3D mesh.

Method of generating surface defined by boundary of three-dimensional point cloud

Bubbles and foam are important fluid phenomena on scales that we encounter in our lives every day. While different techniques to handle these effects were developed in the past years, they require a full 3D fluid solver with free surfaces and surface tension. We present a shallow water based particle model that is coupled with a smoothed particle hydrodynamics simulation to demonstrate that real-time simulations of bubble and foam effects are possible with high frame rates. A shallow water simulation is used to represent the overall water volume. It is coupled to a particle-based bubble simulation with a flow field of spherical vortices. This bubble simulation is interacting with a smoothed particle hydrodynamics simulation including surface tension to handle foam on the fluid surface. The realism and performance of our approach is demonstrated with several test cases that run with high frame rates on a standard PC.

Simon Schirm

Papers

Interaction of fluids with deformable solids

Interactive blood simulation for virtual surgery based on smoothed particle hydrodynamics

Real-time Breaking Waves for Shallow Water Simulations

Method of generating surface defined by boundary of three-dimensional point cloud

Real-time simulations of bubbles and foam within a shallow water framework