Physics-Based Animation

Francois Dagenais, Jonathan Gagnon, Eric Paquette

The simulation of highly viscous fluids using an SPH (Smoothed Particle Hydrodynamics) approach is a tedious task. Since the equations are typically posed as stiff problems, simulating highly viscous fluids involves strong forces applied to the particles. With these strong forces, a very small time step is needed to keep the simulation stable and produce good results. The approach detailed in this paper uses an iterative prediction-correction scheme to optimize forces that act on the fluid, in order to produce a behavior that varies from liquid to solid. This approach significantly reduces the computation times when the fluid is very viscous and almost rigid. At every time step, each particle position is predicted. The deformation is then compared with a target deformation and forces are adjusted to counteract the deformation. In addition to requiring lengthy computation times and tedious adjustment of time step to maintain a stable simulation, typical SPH simulators make it difficult to achieve the desired behavior. This difficulty is caused by the highly non-linear effect that the viscosity has on the behavior of the fluid. Compared to the typical viscosity parameter which varies from zero to infinity, the proposed rigidity parameter is easier to control, providing an intuitive variation from 0 (liquid) to 1 (solid). Since simulating high viscosity fluids is subject to large computation times and instabilities, we complement the proposed model with some important improvements. Firstly, an improved time step adjustment is proposed that results in both reduced computation times and increased stability. Secondly, an implicit temperature diffusion provides stable melting and solidification, regardless of the size of the time step. Thirdly, a constraint propagation provides faster convergence of the rigid forces to visually realistic behaviors. Together, these improvements and the proposed model allow the simulation of fluids with viscous behaviors that were very difficult, if not impossible, to simulate with current SPH approaches.

A Prediction-Correction Approach for Stable SPH Fluid Simulation from Liquid to Rigid

S. Auer, C. B. MacDonald, M. Treib, J. Schneider, R. Westermann

The Closest Point Method (CPM) is a method for numerically solving partial differential equations (PDEs) on arbitrary surfaces, independent of the existence of a surface parametrization. The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well-understood techniques. In this paper, we present the numerical solution of the wave equation and the incompressible Navier-Stokes equations on surfaces via the CPM, and we demonstrate surface appearance and shape variations in real-time using this method. To fully exploit the potential of the CPM, we present a novel GPU realization of the entire CPM pipeline. We propose a surface-embedding adaptive 3D spatial grid for efficient representation of the surface, and present a high-performance approach using CUDA for converting surfaces given by triangulations into this representation. For real-time performance, CUDA is also used for the numerical procedures of the CPM. For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray-casting method that works on the adaptive 3D grid.

Real-Time Fluid Effects on Surfaces using the Closest Point Method

Theodore Kim, Jerry Tessendorf, Nils Thuerey

We propose a method of increasing the apparent spatial resolution of an existing liquid simulation. Previous approaches to this “up-resing” problem have focused on increasing the turbulence of the underlying velocity field. Motivated by measurements in the free surface turbulence literature, we observe that past certain frequencies, it is sufficient to perform a wave simulation directly on the liquid surface, and construct a reduced-dimensional surface-only simulation. We sidestep the considerable problem of generating a surface parameterization by employing an embedding technique known as the Closest Point Method (CPM) that operates directly on a 3D extension field. The CPM requires 3D operators, and we show that for surface operators with no natural 3D generalization, it is possible to construct a viable operator using the inverse Abel transform. We additionally propose a fast,frozen core closest point transform, and an advection method for the extension field that reduces smearing considerably. Finally, we propose two turbulence coupling methods that seed the high resolution wave simulation in visually expected regions.

Closest Point Turbulence for Liquid Surfaces

Pascal Clausen, Martin Wicke, Jonathan Shewchuk, James O’Brien

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.

Simulating Liquids and Solid-Liquid Interaction with Lagrangian Meshes