Iterative algorithms are frequently used to resolve simultaneous impacts between rigid bodies in physical simulations. However, these algorithms lack formal guarantees of termination, which is sometimes viewed as potentially dangerous, so failsafes are used in practical codes to prevent infinite loops. We show such steps are unnecessary. In particular, we study the broad class of such algorithms that are conservative and satisfy a minimal set of physical correctness properties, and which encompasses recent methods like Generalized Reflections as well as pairwise schemes. We fully characterize finite termination of these algorithms. The only possible failure cases can be detected, and we describe a procedure for modifying the algorithms to provably ensure termination. We also describe modifications necessary to guarantee termination in the presence of numerical error due to the use of floating-point arithmetic. Finally, we discuss the challenges dissipation introduce for finite termination, and describe how dissipation models can be incorporated while retaining the termination guarantee.

All’s Well That Ends Well: Guaranteed Resolution of Simultaneous Rigid Body Impact

]]>We present a practical approach for automatically estimating the material properties of soft bodies from two sets of images, taken before and after deformation. We reconstruct 3D geometry from the given sets of multiple-view images; we use a coupled simulation-optimization-identification framework to deform one soft body at its original, non-deformed state to match the deformed geometry of the same object in its deformed state. For shape correspondence, we use a distance-based error metric to compare the estimated deformation fields against the actual deformation field from the reconstructed geometry. The optimal set of material parameters is thereby determined by minimizing the error metric function. This method can simultaneously recover the elasticity parameters of multiple types of soft bodies using Finite Element Method-based simulation (of either linear or nonlinear materials undergoing large deformation) and particle-swarm optimization methods. We demonstrate this approach on real-time interaction with virtual organs in patient-specific surgical simulation, using parameters acquired from low-resolution medical images. We also highlight the results on physics-based animation of virtual objects using sketches from an artist’s conception.

MaterialCloning: Acquiring Elasticity Parameters from Images for Medical Applications

]]>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

]]>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.

]]>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.

]]>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

]]>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.

]]>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.

]]>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

]]>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

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