Category: Fluids

Omri Azencot, Orestis Vantzos and Mirela Ben-Chen

We present a new structure-preserving numerical scheme for solving the Euler–Poincaré Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our method solves the difficult non-linear EPDiff equation by constructing energy preserving, yet fully explicit, update rules. Our approach uses standard differential operators on triangle meshes, allowing for a simple and efficient implementation. Key to the structure-preserving features that our method exhibits is a novel numerical splitting scheme. Namely, we break the integration into three steps which rely on linear solves with a fixed sparse matrix that is independent of the simulation and thus can be pre-factored. We test our method in the context of simulating concentrated reconnecting wavefronts on flat and curved domains. In particular, EPDiff is known to generate geometrical fronts which exhibit wave-like behavior when they interact with each other. In addition, we also show that at a small additional cost, we can produce globally-supported periodic waves by using our simulated fronts with wavefronts tracking techniques. We provide quantitative graphs showing that our method exactly preserves the energy in practice. In addition, we demonstrate various interesting results including annihilation and recreation of a circular front, a wave splitting and merging when hitting an obstacle and two separate fronts propagating and bending due to the curvature of the domain.

An Explicit Structure Preserving numerical scheme for EPDiff

Orestis Vantzos, Saar Raz and Mirela Ben-Chen

We propose a novel discrete scheme for simulating viscous thin films at real-time frame rates. Our scheme is based on a new formulation of the gradient flow approach, that leads to a discretization based on local stencils that are easily computable on the GPU. Our approach has physical fidelity, as the total mass is guaranteed to be preserved, an appropriate discrete energy is controlled, and the film height is guaranteed to be non-negative at all times. In addition, and unlike all existing methods for thin films simulation, it is fast enough to allow realtime interaction with the flow, for designing initial conditions and controlling the forces during the simulation.

Real-Time Viscous Thin Films

Syuhei Sato, Yoshinori Dobashi, Tomoyuki Nishita

The computational cost for creating realistic fluid animations by numerical simulation is generally expensive. In digital production environments, existing precomputed fluid animations are often reused for different scenes in order to reduce the cost of creating scenes containing fluids. However, applying the same animation to different scenes often produces unacceptable results, so the animation needs to be edited. In order to help animators with the editing process, we develop a novel method for synthesizing the desired fluid animations by combining existing flow data. Our system allows the user to place flows at desired positions, and combine them. We do this by interpolating velocities at the boundaries between the flows. The interpolation is formulated as a minimization problem of an energy function, which is designed to take into account the inviscid, incompressible Navier-Stokes equations. Our method focuses on smoke simulations defined on a uniform grid. We demonstrate the potential of our method by showing a set of examples, including a large-scale sandstorm created from a few flow data simulated in a small-scale space.

Editing Fluid Animation Using Flow Interpolation

Chinmayee Shah, David Hyde, Hang Qu, and Philip Levis

This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a low resolution simulation in parallel. This paper describes a system design and techniques to automatically distribute and load balance sparse fluid simulations, and presents speculative load balancing, a general technique to effectively balance future load using information about future load distribution obtained via a low resolution simulation. We mathematically formulate the problem of load balancing over multiple time-steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.5x to 7.2x, and that speculative load balancing generates assignments that perform within 20% of optimal.

Distributing and Load Balancing Sparse Fluid Simulations

Marie-Lena Eckert, Wolfgang Heidrich, Nils Thuerey

We present a novel method to reconstruct a fluid’s 3D density and motion based on just a single sequence of images. This is rendered possible by using powerful physical priors for this strongly under-determined problem. More specifically, we propose a novel strategy to infer density updates strongly coupled to previous and current estimates of the flow motion. Additionally, we employ an accurate discretization and depth-based regularizers to compute stable solutions. Using only one view for the reconstruction reduces the complexity of the capturing setup drastically and could even allow for online video databases or smart-phone videos as inputs. The reconstructed 3D velocity can then be flexibly utilized, e.g., for re-simulation, domain modification or guiding purposes. We will demonstrate the capacity of our method with a series of synthetic test cases and the reconstruction of real smoke plumes captured with a Raspberry Pi camera.

Coupled Fluid Density and Motion from Single Views