Category: Fluids

Shengfeng He, Rynson W. H. Lau

Capturing fine details of turbulence on a coarse grid is one of the main tasks in real-time fluid simulation. Existing methods for doing this have various limitations. In this paper, we propose a new turbulence method that uses a refined Second Vorticity Confinement method, referred to as Robust Second Vorticity Confinement, and a synthesis scheme to create highly turbulent effects from coarse grid. The new technique is sufficiently stable to efficiently produce highly turbulent flows, while allowing intuitive control of vortical structures. Second Vorticity Confinement captures and defines the vortical features of turbulence on a coarse grid. However, due to the stability problem, it cannot be used to produce highly turbulent flows. In this work, we propose a robust formulation to improve the stability problem by making the positive diffusion term to vary with helicity adaptively. In addition, we also employ our new method to procedurally synthesize the high resolution flow fields. As shown in our results, this approach produces stable high resolution turbulence very efficiently.

Synthetic Controllable Turbulence Using Robust Second Vorticity Confinement

Ryoichi Ando, Nils Thürey and Chris Wojtan

We introduce a new method for efficiently simulating liquid with extreme amounts of spatial adaptivity. Our method combines several key components to drastically speed up the simulation of large-scale fluid phenomena: We leverage an alternative Eulerian tetrahedral mesh discretization to significantly reduce the complexity of the pressure solve while increasing the robustness with respect to element quality and removing the possibility of locking. Next, we enable subtle free-surface phenomena by deriving novel second-order boundary conditions consistent with our discretization. We couple this discretization with a spatially adaptive Fluid-Implicit Particle (FLIP) method, enabling efficient, robust, minimally-dissipative simulations that can undergo sharp changes in spatial resolution while minimizing artifacts. Along the way, we provide a new method for generating a smooth and detailed surface from a set of particles with variable sizes. Finally, we explore several new sizing functions for determining spatially adaptive simulation resolutions, and we show how to couple them to our simulator. We combine each of these elements to produce a simulation algorithm that is capable of creating animations at high maximum resolutions while avoiding common pitfalls like inaccurate boundary conditions and inefficient computation.

Highly Adaptive Liquid Simulations on Tetrahedral Meshes

Michael B. Nielsen, Ole Osterby

Physics based simulation of the dynamics of water spray – water droplets dispersed in air – is a means to increase the visual plausibility of computer graphics modeled phenomena such as waterfalls, water jets and stormy seas. Spray phenomena are frequently encountered by the visual effects industry and often challenge state of the art methods. Current spray simulation pipelines typically employ a combination of Lagrangian (particle) and Eulerian (volumetric) methods – the Eulerian methods being used for parts of the spray where individual droplets are not apparent. However, existing Eulerian methods in computer graphics are based on gas solvers that will for example exhibit hydrostatic equilibrium in certain scenarios where the air is expected to rise and the water droplets fall. To overcome this problem, we propose to simulate spray in the Eulerian domain as a two-way coupled two-continua of air and water phases co-existing at each point in space. The fundamental equations originate in applied physics and we present a number of contributions that make Eulerian two-continua spray simulation feasible for computer graphics applications. The contributions include a Poisson equation that fits into the operator splitting methodology as well as (semi-)implicit discretizations of droplet diffusion and the drag force with improved stability properties. As shown by several examples, our approach allows us to more faithfully capture the dynamics of spray than previous Eulerian methods.

A Two-Continua Approach to Eulerian Simulation of Water Spray

Matt Stanton, Yu Sheng, Martin Wicke, Federico Perazzi, Amos Yuen, Srinivasa Narasimhan, Adrien Treuille

This paper extends Galerkin projection to a large class of non-polynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.

Non-Polynomial Galerkin Projection on Deforming Meshes

Miles Macklin, Matthias Müller

In fluid simulation, enforcing incompressibility is crucial for realism; it is also computationally expensive. Recent work has improved efficiency, but still requires time-steps that are impractical for real-time applications. In this work we present an iterative density solver integrated into the Position Based Dynamics framework (PBD). By formulating and solving a set of positional constraints that enforce constant density, our method allows similar incompressibility and convergence to modern smoothed particle hydrodynamic (SPH) solvers, but inherits the stability of the geometric, position based dynamics method, allowing large time steps suitable for real-time applications. We incorporate an artificial pressure term that improves particle distribution, creates surface tension, and lowers the neighborhood requirements of traditional SPH. Finally, we address the issue of energy loss by applying vorticity confinement as a velocity post process.

Position Based Fluids

Morten Bojsen-Hansen, Chris Wojtan

Our work concerns the combination of an Eulerian liquid simulation with a high-resolution surface tracker (e.g. the level set method or a Lagrangian triangle mesh). The naive application of a high-resolution surface tracker to a low-resolution velocity field can produce many visually disturbing physical and topological artifacts that limit their use in practice. We address these problems by defining an error function which compares the current state of the surface tracker to the set of physically valid surface states. By reducing this error with a gradient descent technique, we introduce a novel physics-based surface fairing method. Similarly, by treating this error function as a potential energy, we derive a new surface correction force that mimics the vortex sheet equations. We demonstrate our results with both level set and mesh-based surface trackers.

Liquid Surface Tracking with Error Compensation

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