Category: Fluids

A Positive-Definite Cut-Cell Method for Strong Two-Way Coupling Between Fluids and Deformable Bodies

Omar Zarifi, Christopher Batty

We present a new approach to simulation of two-way coupling between inviscid free surface fluids and deformable bodies that exhibits several notable advantages over previous techniques. By fully incorporating the dynamics of the solid into pressure projection, we simultaneously handle fluid incompressibility and solid elasticity and damping. Thanks to this strong coupling, our method does not suer from instability, even in very taxing scenarios. Furthermore, use of a cut-cell discretization methodology allows us to accurately apply proper free-slip boundary conditions at the exact solid-fluid interface. Consequently, our method is capable of correctly simulating inviscid tangential flow, devoid of grid artefacts or artificial sticking. Lastly, we present an efficient algebraic transformation to convert the indenite coupled pressure projection system into a positive-definite form. We demonstrate the efficacy of our proposed method by simulating several interesting scenarios, including a light bath toy colliding with a collapsing column of water, liquid being dropped onto a deformable platform, and a partially liquid-filled deformable elastic sphere bouncing.

A Positive-Definite Cut-Cell Method for Strong Two-Way Coupling Between Fluids and Deformable Bodies

A Micropolar Material Model for Turbulent SPH Fluids

Jan Bender, Dan Koschier, Tassilo Kugelstadt, Marcel Weiler

In this paper we introduce a novel micropolar material model for the simulation of turbulent inviscid fluids. The governing equations are solved by using the concept of Smoothed Particle Hydrodynamics (SPH). As already investigated in previous works, SPH fluid simulations suffer from numerical diffusion which leads to a lower vorticity, a loss in turbulent details and finally in less realistic results. To solve this problem we propose a micropolar fluid model. The micropolar fluid model is a generalization of the classical Navier-Stokes equations, which are typically used in computer graphics to simulate fluids. In contrast to the classical Navier-Stokes model, micropolar fluids have a microstructure and therefore consider the rotational motion of fluid particles. In addition to the linear velocity field these fluids also have a field of microrotation which represents existing vortices and provides a source for new ones. However, classical micropolar materials are viscous and the translational and the rotational motion are coupled in a dissipative way. Since our goal is to simulate turbulent fluids, we introduce a novel modified micropolar material for inviscid fluids with a non-dissipative coupling. Our model can generate realistic turbulences, is linear and angular momentum conserving, can be easily integrated in existing SPH simulation methods and its computational overhead is negligible.

A Micropolar Material Model for Turbulent SPH Fluids

Evaporation and Condensation of SPH-based Fluids

Hendrik Hochstetter, Andreas Kolb

In this paper we present a method to simulate evaporation and condensation of liquids. Therefore, both the air and liquid phases have to be simulated. We use, as a carrier of vapor, a coarse grid for the air phase and mass-preservingly couple it to an SPH-based liquid and rigid body simulation. Since condensation only takes place on rigid surfaces, it is captured using textures that carry water to achieve high surface detail. The textures can exchange water with the air phase and are used to generate new particles due to condensation effects yielding a full two-way coupling of air phase and liquid. In order to allow gradual evaporation and condensation processes, liquid particles can take on variable sizes. Our proposed improved implicit surface definition is able to render dynamic contact angles for moving droplets yielding highly detailed fluid rendering.

Evaporation and Condensation of SPH-based Fluids

Fully Asynchronous SPH Simulation

Stefan Reinhardt, Markus Huber, Bernhard Eberhardt, Daniel Weiskopf

We present a novel method for fully asynchronous time integration of particle-based fluids using smoothed particle hydrodynamics (SPH). With our approach, we allow a dedicated time step for each particle. Therefore, we are able to increase the efficiency of simulations. Previous approaches of locally adaptive time steps have shown promising results in the form of increased time steps, however, they need to synchronize time steps in recurring intervals, which involves either interpolation operations or matching time steps. With our method, time steps are asynchronous through the whole simulation and no global time barriers are needed. In addition, we present an efficient method for parallelization of our novel asynchronous time integration. For both serial and parallel execution, we achieve speedups of up to 7.5 compared to fixed time steps and are able to outperform previous adaptive approaches considerably

Fully Asynchronous SPH Simulation

Density Maps for Improved SPH Boundary Handling

Dan Koschier, Jan Bender

In this paper, we present the novel concept of density maps for robust handling of static and rigid dynamic boundaries in fluid simulations based on Smoothed Particle Hydrodynamics (SPH). In contrast to the vast majority of existing approaches, we use an implicit discretization for a continuous extension of the density field throughout solid boundaries. Using the novel representation we enhance accuracy and efficiency of density and density gradient evaluations in boundary regions by computationally efficient lookups into our density maps. The map is generated in a preprocessing step and discretizes the density contribution in the boundary’s near-field. In consequence of the high regularity of the continuous boundary density field, we use cubic Lagrange polynomials on a narrow-band structure of a regular grid for discretization. This strategy not only removes the necessity to sample boundary surfaces with particles but also decouples the particle size from the number of sample points required to represent the boundary. Moreover, it solves the ever-present problem of particle deficiencies near the boundary. In several comparisons we show that the representation is more accurate than particle samplings, especially for smooth curved boundaries. We further demonstrate that our approach robustly handles scenarios with highly complex boundaries and even outperforms one of the most recent sampling based techniques.

Density Maps for Improved SPH Boundary Handling

Water Wave Packets

Stefan Jeschke, Chris Wojtan

This paper presents a method for simulating water surface waves as a displacement field on a 2D domain. Our method relies on Lagrangian particles that carry packets of water wave energy; each packet carries information about an entire group of wave trains, as opposed to only a single wave crest. Our approach is unconditionally stable and can simulate high resolution geometric details. This approach also presents a straightforward interface for artistic control, because it is essentially a particle system with intuitive parameters like wavelength and amplitude. Our implementation parallelizes well and runs in real time for moderately challenging scenarios.

Water Wave Packets

A Schur Complement Preconditioner for Scalable Parallel Fluid Simulation

Jieyu Chu, Nafees Bin Zafar, Xubo Yang

We present an algorithmically efficient and parallelized domain decomposition based approach to solving Poisson’s equation on irregular domains. Our technique employs the Schur complement method, which permits a high degree of parallel efficiency on multi-core systems. We create a novel Schur complement preconditioner which achieves faster convergence, and requires less computation time and memory. This domain decomposition method allows us to apply different linear solvers for different regions of the flow. Subdomains with regular boundaries can be solved with an FFT based Fast Poisson Solver. We can solve systems with 10243 degrees of freedom, and demonstrate its use for the pressure projection step of incompressible liquid and gas simulations. The results demonstrate considerable speedup over preconditioned conjugate gradient methods commonly employed to solve such problems, including a multigrid preconditioned conjugate gradient method.

A Schur Complement Preconditioner for Scalable Parallel Fluid Simulation

Efficient Optimal Control of Smoke using Spacetime Multigrid

Zherong Pan and Dinesh Manocha

We present a novel algorithm to control the physically-based animation of smoke. Given a set of keyframe smoke shapes, we compute a dense sequence of control force fields that can drive the smoke shape to match several keyframes at certain time instances. Our approach formulates this control problem as a PDE constrained spacetime optimization and computes locally optimal control forces as the stationary point of the Karush-Kuhn-Tucker conditions. In order to reduce the high complexity of multiple passes of fluid resimulation, we utilize the coherence between consecutive fluid simulation passes and update our solution using a novel spacetime full approximation scheme (STFAS). We demonstrate the benefits of our approach by computing accurate solutions on 2D and 3D benchmarks. In practice, we observe more than an order of magnitude improvement over prior methods.

Efficient Optimal Control of Smoke using Spacetime Multigrid

Fluxed Animated Boundary Method

Alexey Stomakhin, Andrew Selle

We present a novel approach to guiding physically based particle simulations using boundary conditions. Unlike commonly used ad hoc particle techniques for adding and removing the material from a simulation, our approach is principled by utilizing the concept of volumetric flux. Artists are provided with a simple yet powerful primitive called a fluxed animated boundary (FAB), allowing them to specify a control shape and a material flow field. The system takes care of enforcing the corresponding boundary conditions and necessary particle reseeding. We show how FABs can be used artistically or physically. Finally, we demonstrate production examples that show the efficacy of our method.

Fluxed Animated Boundary Method

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact

Chenfanfu Jiang, Theodore Gast, Joseph Teran

The typical elastic surface or curve simulation method takes a Lagrangian approach and consists of three components: time integration, collision detection and collision response. The Lagrangian view is beneficial because it naturally allows for tracking of the codimensional manifold, however collision must then be detected and resolved separately. Eulerian methods are promising alternatives because collision processing is automatic and while this is effective for volumetric objects, advection of a codimensional manifold is too inaccurate in practice. We propose a novel hybrid Lagrangian/Eulerian approach that preserves the best aspects of both views. Similar to the Drucker-Prager and Mohr-Coulomb models for granular materials, we define our collision response with a novel elastoplastic constitutive model. To achieve this, we design an anisotropic hyperelastic constitutive model that separately characterizes the response to manifold strain as well as shearing and compression in the directions orthogonal to the manifold. We discretize the model with the Material Point Method and a novel codimensional Lagrangian/Eulerian update of the deformation gradient. Collision intensive scenarios with millions of degrees of freedom require only a few minutes per frame and examples with up to one million degrees of freedom run in less than thirty seconds per frame.

Anisotropic Elastoplasticity for Cloth, Knit and Hair Frictional Contact