Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

Marek Misztal, Kenny Erleben, Adam Bargteil, J. Fursund, Brian Bunch Christensen, Andreas Bærentzen, Robert Bridson

In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method

Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

Linear-Time Smoke Animation with Vortex Sheet Meshes

Tyson Brochu, Todd Keeler, Robert Bridson

We present the first quality physics-based smoke animation method which runs in time approximately linear in the size of the rendered two-dimensional visual detail. Our fundamental representation is a closed triangle mesh surface dividing space between clear air and a uniformly smoky region, on which we compute vortex sheet dynamics to accurately solve inviscid buoyant flow. We handle arbitrary moving no-stick solid boundaries and by default handle an infinite domain. The simulation itself runs in time linear to the number of triangles thanks to the use of a well-conditioned integral equation treatment together with a Fast Multipole Method for linear-time summations, providing excellent performance. Basic zero-albedo smoke rendering, with embedded solids, is easy to implement for interactive rates, and the mesh output can also serve as an extremely compact and detailed input to more sophisticated volume rendering.

Linear-Time Smoke Animation with Vortex Sheet Meshes

SCA 2012

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Topology Adaptive Interface Tracking Using the Deformable Simplicial Complex

Marek Misztal, Andreas Baerentzen

We present a novel, topology-adaptive method for deformable interface tracking, called the Deformable Simplicial Complex (DSC). In the DSC method, the interface is represented explicitly as a piecewise linear curve (in 2D) or surface (in 3D) which is a part of a discretization (triangulation/tetrahedralization) of the space, such that the interface can be retrieved as a set of faces separating triangles/tetrahedra marked as inside from the ones marked as outside (so it is also given implicitly). This representation allows robust topological adaptivity and, thanks to the explicit representation of the interface, it suffers only slightly from numerical diffusion. Furthermore, the use of an unstructured grid yields robust adaptive resolution. Also, topology control is simple in this setting. We present the strengths of the method in several examples: simple geometric flows, fluid simulation, point cloud reconstruction, and cut locus construction.

Topology Adaptive Interface Tracking using the Deformable Simplicial Complex

Energy-Based Self-Collision Culling for Arbitrary Mesh Deformations

Changxi Zheng, Doug James

In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we precompute Energy-based Self-Collision Culling (ESCC) certificates on bounding-volume-related sub-meshes which indicate the amount of deformation energy required for it to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate preprocess, and fast runtime energy evaluation. The latter is performed hierarchically to amortize Laplacian energy and affine-frame estimation computations. ESCC supports both discrete and continuous SCD with detailed and nonsmooth geometry. We demonstrate significant culling on various examples, with SCD speed-ups up to 26X.

Energy-Based Self-Collision Culling for Arbitrary Mesh Deformation

Interactive Space-Time Control of Deformable Objects

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier

Creating motions of objects or characters that are physically plausible and follow an animator’s intent is a key task in computer animation. The spacetime constraints paradigm is a valuable approach to this problem, but it suffers from high computational costs. Based on spacetime constraints, we propose a framework for controlling the motion of deformable objects that offers interactive response times. This is achieved by a model reduction of the underlying variational problem, which combines dimension reduction, multipoint linearization, and decoupling of ODEs. After a preprocess, the cost for creating or editing a motion is reduced to solving a number of one-dimensional spacetime problems, whose solutions are the wiggly splines introduced by Kass and Anderson [2008]. We achieve interactive response times through a new fast and robust numerical scheme for solving the one-dimensional problems that is based on a closed-form representation of the wiggly splines.

Interactive Space-Time Control of Deformable Objects

Versatile Rigid-Fluid Coupling for Incompressible SPH

Nadir Akinci, Markus Ihmsen, Gizem Akinci, Barbara Solenthaler, Matthias Teschner

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

Adaptive Image-Based Intersection Volume

Bin Wang, Francois Faure, Dinesh Pai

A method for image-based contact detection and modeling, with guaranteed precision on the intersection volume, is presented. Unlike previous image-based methods, our method optimizes a non-uniform ray sampling resolution and allows precise control of the volume error. By cumulatively projecting all mesh edges into a generalized 2D texture, we construct a novel data structure, the Error Bound Polynomial Image (EBPI), which allows efficient computation of the maximum volume error as a function of ray density. Based on a precision criterion, EBPI pixels are subdivided or clustered. The rays are then cast in the projection direction according to the non-uniform resolution. The EBPI data, combined with ray-surface intersection points and normals, is also used to detect transient edges at surface intersections. This allows us to model intersection volumes at arbitrary resolution, while avoiding the geometric computation of mesh intersections. Moreover, the ray casting acceleration data structures can be reused for the generation of high quality images.

Adaptive Image-Based Intersection Volume

Fast Simulation of Skeleton-Driven Deformable Body Characters

Junggon Kim, Nancy Pollard

We propose a fast physically based simulation system for skeleton-driven deformable body characters. Our system can generate realistic motions of self-propelled deformable body characters by considering the two-way interactions among the skeleton, the deformable body, and the environment in the dynamic simulation. It can also compute the passive jiggling behavior of a deformable body driven by a kinematic skeletal motion. We show that a well-coordinated combination of (1) a reduced deformable body model with nonlinear finite elements, (2) a linear-time algorithm for skeleton dynamics, and (3) explicit integration can boost simulation speed to orders of magnitude faster than existing methods, while preserving modeling accuracy as much as possible. Parallel computation on the GPU has also been implemented to obtain an additional speedup for complicated characters. Detailed discussions of our engineering decisions for speed and accuracy of the simulation system are presented in the paper. We tested our approach with a variety of skeleton-driven deformable body characters, and the tested characters were simulated in real-time or near real-time.

Fast Simulation of Skeleton-Driven Deformable Body Characters