Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes

Abstract

Figure 1: Multiple fluids with different viscosity coefficients and surface tension densities splashing on the bottom of a cylindrical container. Observe that the simulation has no problem dealing with thin sheets. AbstractIn 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.

Fast multiple-fluid simulation using Helmholtz free energy

“…[Hong and Kim 2005;Losasso et al 2006;Kim 2010;Boyd and Bridson 2012;Misztal et al 2012;Bao et al 2010;Kang et al 2010] assume incompressibility with the divergence-free condition and work well on topological transitions, thus achieving plausible results. Previously, the smoothed particle hydrodynamics (SPH) method [Monaghan 1992;Monaghan 1994] gained popularity as a particle based method among the graphics community due to its properties of mass-conservation and easy-to-handle Lagrangian discretization.…”

“…Solenthaler and Pajarola [2008] improved the standard SPH method to deal with density contrast more precisely. Amongst Eulerian approaches, the level-set method, the volume-of-fluid (VOF) method, and the finite element method are widely used for interface tracking between phases or components [Hong and Kim 2005;Losasso et al 2006;Kim 2010;Boyd and Bridson 2012;Misztal et al 2012].…”

“…Previous works on multiple-fluid simulation can be divided into two main categories focusing on either immiscible fluids or on miscible or dispersed fluids. In the former category, clear interfaces exist between different phases, and many works (e.g., [Hong and Kim 2005;Losasso et al 2006;Kim 2010;Boyd and Bridson 2012;Misztal et al 2012;Da et al 2014]) have obtained visually plausible results by tracking the interfaces. However, in the latter category, there are no clear interfaces between different phases, and the volume fraction method [Müller et al 2005] has been widely adopted.…”

Multimaterial mesh-based surface tracking

“…[Quan and Schmidt 2007;Pons and Boissonnat 2007a;Pons and Boissonnat 2007b;Quan et al 2009;Misztal et al 2012] assign material labels to each volume element. For example, for a tetrahedralization of space, the interface is the subset of triangular faces bordering two differently labeled tetrahedra.…”

Multiphase Image Segmentation Using the Deformable Simplicial Complex Method

“…The DSC method is implemented in 2D and 3D, and has application in fluid simulation [3], [4], topology optimization [5] and computing cut loci on Riemannian manifolds [6]. In this paper we present an initial investigation in using 2D DSC for image segmentation.…”