research-article

Model-reduced variational fluid simulation

Authors:

Julian Hodgson,

Mathieu DesbrunAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 34, Issue 6

Article No.: 244, Pages 1 - 12

https://doi.org/10.1145/2816795.2818130

Published: 02 November 2015 Publication History

Abstract

We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar- and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains.

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Index Terms

Model-reduced variational fluid simulation
1. Computing methodologies
  1. Computer graphics
    1. Animation

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 34, Issue 6

November 2015

944 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2816795

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Copyright © 2015 ACM.

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Published: 02 November 2015

Published in�TOG�Volume 34, Issue 6

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Mo HGao CWang R(2024)Joint Stroke Tracing and Correspondence for 2D AnimationACM Transactions on Graphics10.1145/364989043:3(1-17)Online publication date: 9-Apr-2024
https://dl.acm.org/doi/10.1145/3649890
Kumar Singh SRai RPradip Khawale RPatel DBielecki DNguyen RWang JZhang Z(2024)Deep Learning in Computational Design Synthesis: A Comprehensive ReviewJournal of Computing and Information Science in Engineering10.1115/1.406421524:4Online publication date: 8-Jan-2024
https://doi.org/10.1115/1.4064215
Willett Nde Goes FFleischer KMeyer MBurrows C(2024)Stylizing Ribbons: Computing Surface Contours With Temporally Coherent OrientationsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.330464130:8(5623-5634)Online publication date: 1-Aug-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3304641
Lv CLin WZheng J(2024)Adaptively Isotropic Remeshing Based on Curvature Smoothed FieldIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.322797030:7(3196-3209)Online publication date: 1-Jul-2024
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