A Multiscale Approach to Mesh-based Surface Tension

We present an approach to simulate flows driven by surface tension based on triangle meshes. Our method consists of two simulation layers: the first layer is an Eulerian method for simulating surface tension forces that is free from typical strict time step constraints. The second simulation layer is a Lagrangian finite element method that simulates sub-grid scale wave details on the fluid surface. The surface wave simulation employs an unconditionally stable, symplectic time integration method that allows for a high propagation speed due to strong surface tension. Our approach can naturally separate the grid- and sub-grid scales based on a volume-preserving mean curvature flow. As our model for the sub-grid dynamics enforces a local conservation of mass, it leads to realistic pinch off and merging effects. In addition to this method for simulating dynamic surface tension effects, we also present an efficient non-oscillatory approximation for capturing damped surface tension behavior. These approaches allow us to efficiently simulate complex phenomena associated with strong surface tension, such as Rayleigh-Plateau instabilities and crown splashes, in a short amount of time.

A Multiscale Approach to Mesh-based Surface Tension

Unified Simulation of Elastic Rods, Shells, and Solids

We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.

Unified Simulation of Elastic Rods, Shells, and Solids

Matching Fluid Simulation Elements to Surface Geometry and Topology

We introduce an Eulerian liquid simulation framework based on the Voronoi diagram of a potentially unorganized collection of pressure samples. Constructing the simulation mesh in this way allows us to place samples anywhere in the computational domain; we exploit this by choosing samples that accurately capture the geometry and topology of the liquid surface. When combined with high-resolution explicit surface tracking this allows us to simulate nearly arbitrarily thin features, while eliminating noise and other artifacts that arise when there is a resolution mismatch between the simulation and the surface—and allowing a precise inclusion of surface tension based directly on and at the same resolution as the surface mesh. In addition, we present a simplified Voronoi/Delaunay mesh velocity interpolation scheme, and a direct extension of embedded free surfaces and solid boundaries to Voronoi meshes.

Matching Fluid Simulation Elements to Surface Geometry and Topology

SCA 2006

Physics-related papers from SCA 2006. The full list is available here, courtesy of Kesen-Huang.

Eurographics 2008

Physics-oriented papers from Eurographics 2008.

Short papers:

SCA 2007

Still filling in some older collections… Kesen maintains a complete list here.

Eurographics 2009 papers

Looking backwards again… Kesen’s full page is here.

SIGGRAPH 2006 papers

I noticed today that I’d catalogued physics papers from conferences between 2007 and the present, and that Simon Clavet had catalogued a large number of physics papers from various conferences prior to 2006, with some going back as far as 1992.  So in the interests of completeness, I thought I’d fill in a list for SIGGRAPH 2006.   Clearly Kesen maintains a more thorough list covering all of graphics, but I sometimes find it helpful to see just the physics ones alone.  (I might add a few of the other conferences/years I’ve missed at some point as well.)

Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids

When simulating fluids, tetrahedral methods provide flexibility and ease of adaptivity that Cartesian grids find difficult to match. However, this approach has so far been limited by two conflicting requirements. First, accurate simulation requires quality Delaunay meshes and the use of circumcentric pressures. Second, meshes must align with potentially complex moving surfaces and boundaries, necessitating continuous remeshing. Unfortunately, sacrificing mesh quality in favour of speed yields inaccurate velocities and simulation artifacts. We describe how to eliminate the boundary-matching constraint by adapting recent embedded boundary techniques to tetrahedra, so that neither air nor solid boundaries need to align with mesh geometry. This enables the use of high quality, arbitrarily graded, non-conforming Delaunay meshes, which are simpler and faster to generate. Temporal coherence can also be exploited by reusing meshes over adjacent timesteps to further reduce meshing costs. Lastly, our free surface boundary condition eliminates the spurious currents that previous methods exhibited for slow or static scenarios. We provide several examples demonstrating that our efficient tetrahedral embedded boundary method can substantially increase the flexibility and accuracy of adaptive Eulerian fluid simulation.

Tetrahedral Embedded Boundary Methods for Accurate and Flexible Adaptive Fluids