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

We present a novel, incompressible fluid simulation method based on the Lagrangian Smoothed Particle Hydrodynamics (SPH) model. In our method, incompressibility is enforced by using a prediction-correction scheme to determine the particle pressures. For this, the information about density fluctuations is actively propagated through the fluid and pressure values are updated until the targeted density is satisfied. With this approach, we avoid the computational expenses of solving a pressure Poisson equation, while still being able to use large time steps in the simulation. The achieved results show that our predictive-corrective incompressible SPH (PCISPH) method clearly outperforms the commonly used weakly compressible SPH (WCSPH) model by more than an order of magnitude while the computations are in good agreement with the WCSPH results.

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Predictive-corrective incompressible SPH

We propose a momentum-conserving two-way coupling method of SPH fluids and arbitrary rigid objects based on hydrodynamic forces. Our approach samples the surface of rigid bodies with boundary particles that interact with the fluid, preventing deficiency issues and both spatial and temporal discontinuities. The problem of inhomogeneous boundary sampling is addressed by considering the relative contribution of a boundary particle to a physical quantity. This facilitates not only the initialization process but also allows the simulation of multiple dynamic objects. Thin structures consisting of only one layer or one line of boundary particles, and also non-manifold geometries can be handled without any additional treatment. We have integrated our approach into WCSPH and PCISPH, and demonstrate its stability and flexibility with several scenarios including multiphase flow.

Versatile rigid-fluid coupling for incompressible SPH

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

Implicit Incompressible SPH

We present a new method for the simulation of melting and solidification in a unified particle model. Our technique uses the Smoothed Particle Hydrodynamics (SPH) method for the simulation of liquids, deformable as well as rigid objects, which eliminates the need to define an interface for coupling different models. Using this approach, it is possible to simulate fluids and solids by only changing the attribute values of the underlying particles. We significantly changed a prior elastic particle model to achieve a flexible model for melting and solidification. By using an SPH approach and considering a new definition of a local reference shape, the simulation of merging and splitting of different objects, as may be caused by phase change processes, is made possible. In order to keep the system stable even in regions represented by a sparse set of particles we use a special kernel function for solidification processes. Additionally, we propose a surface reconstruction technique based on considering the movement of the center of mass to reduce rendering errors in concave regions. The results demonstrate new interaction effects concerning the melting and solidification of material, even while being surrounded by liquids.

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A unified particle model for fluid–solid interactions

We present a new method for the simulation of melting and solidification in a unified particle model. Our technique uses the Smoothed Particle Hydrodynamics (SPH) method for the simulation of liquids, deformable as well as rigid objects, which eliminates the need to define an interface for coupling different models. Using this approach, it is possible to simulate fluids and solids by only changing the attribute values of the underlying particles. We significantly changed a prior elastic particle model to achieve a flexible model for melting and solidification. By using an SPH approach and considering a new definition of a local reference shape, the simulation of merging and splitting of different objects, as may be caused by phase change processes, is made possible. In order to keep the system stable even in regions represented by a sparse set of particles we use a special kernel function for solidification processes. Additionally, we propose a surface reconstruction technique based on considering the movement of the center of mass to reduce rendering errors in concave regions. The results demonstrate new interaction effects concerning the melting and solidification of material, even while being surrounded by liquids. Copyright © 2007 John Wiley & Sons, Ltd.

Jürg Schläfli

Papers

A unified particle model for fluid–solid interactions

A unified particle model for fluid–solid interactions: Research Articles