Lagrangian vortex sheets for animating fluids

Abstract

Figure 1: A dense cloud subject to buoyancy forces and interaction with a moving obstacle is simulated. We use a Eulerian solver to compute a base flow, as shown on the left. Small-scale detail is synthesized directly on the interface of the cloud. An adapted turbulence model provides details from obstacle interaction (middle left), while small-scale buoyancy effects are calculated using vortex sheet dynamics (in the middle right). The picture on the right shows the combined model. AbstractBuoyant turbulent smoke plumes with a sharp smoke-air interface, such as volcanic plumes, are notoriously hard to simulate. The surface clearly shows small-scale turbulent structures which are costly to resolve. In addition, the turbulence onset is directly visible at the interface, and is not captured by commonly used turbulence models. We present a novel approach that employs a triangle mesh as a highresolution surface representation combined with a coarse Eulerian solver. On the mesh, we solve the interfacial vortex sheet equations, which allows us to accurately simulate buoyancy induced turbulence. For complex boundary conditions we propose an orthogonal turbulence model that handles vortices caused by obstacle interaction. In addition, we demonstrate a re-sampling scheme to remove surfaces that are hidden inside the bulk volume. In this way we are able to achieve highly detailed simulations of turbulent plumes efficiently.

Unified particle physics for real-time applications

“…More recently, Lagrangian discretizations for smoke have gained interest in computer graphics, notably vortex methods such as [Park and Kim 2005], and mesh-tracking methods [Pfaff et al 2012] [Brochu et al 2012]. Stam and Fiume [1995] were the first to apply SPH to the simulation of gas and fire, and Gao et al [2009] combined SPH with a grid-based fluid solver to simulate fast moving gases.…”

“…In this section, we present a turbulence model inspired by the Lagrangian vortex sheets method [Pfaff et al 2012]. Unlike meshtracking methods, we do not have an explicit surface representation, instead we use the following unnormalized vector as an approximate surface normal…”

Reducing numerical dissipation in smoke simulation

“…In fact, there are already some pure particle methods for fluid simulation, such as smoothed particle hydrodynamics (SPH) [54] and some pure vortex particle methods [55]. Several vortex particle methods employ geometry structures to describe vortex structure including filament [56,57], ring [58,59] and sheet [60] to capture various subtle features such as leapfrogging vortex rings and vortex shedding, which are difficult to simulate using the grid-based methods. However, apart from their specified problems such as particle redistribution, pure particle methods cannot enforce incompressible condition as efficient and accurate as the grid methods.…”

A Cut‐Cell Geometric Multigrid Poisson Solver for Fluid Simulation

“…Pfaff et al [PTSG09] proposed to inject the precomputed effects of artificial boundary layers into the simulation to achieve sub-grid motion. Later they used triangular meshes to model the interface between distinct phases [PTG12]. On this representation turbulent behavior is directly synthesized by applying vortex sheet dynamics.…”