More Web Proxy on the site http://driver.im/

research-article

A Second-Order Advection-Reflection Solver

Authors:

Bernhard ThomaszewskiAuthors Info & Claims

Proceedings of the ACM on Computer Graphics and Interactive Techniques, Volume 2, Issue 2

Article No.: 16, Pages 1 - 14

https://doi.org/10.1145/3340257

Published: 26 July 2019 Publication History

Abstract

Zehnder et al. [2018] recently introduced an advection-reflection method for fluid simulation that dramatically reduces artificial dissipation. We establish a connection between their method and the implicit midpoint time integration scheme, and present a simple modification to obtain an advection-reflection scheme with second-order accuracy in time. We compare with existing alternatives, including a second-order semi-Lagrangian method based on BDF2, and demonstrate the improved energy-preservation properties.

Supplementary Material

narain (narain.zip)

Supplemental movie, appendix, image and software files for, A Second-Order Advection-Reflection Solver

Download
154.29 MB

References

[1]

Alexis Angelidis and Fabrice Neyret. 2005. Simulation of Smoke Based on Vortex Filament Primitives. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA '05). 87--96.

Digital Library

[2]

Uri M. Ascher and Linda R. Petzold. 1998. Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations. SIAM.

Digital Library

[3]

Robert Bridson. 2015. Fluid Simulation for Computer Graphics (2nd ed.). CRC Press.

Digital Library

[4]

Albert Chern, Felix Knöppel, Ulrich Pinkall, Peter Schröder, and Steffen Weißmann. 2016. Schrödinger's Smoke. ACM Trans. Graph. 35, 4 (July 2016), 77:1--77:13.

Digital Library

[5]

Qiaodong Cui, Pradeep Sen, and Theodore Kim. 2018. Scalable Laplacian Eigenfluids. ACM Trans. Graph. 37, 4, Article 87 (July 2018), 12 pages.

Digital Library

[6]

Tyler De Witt, Christian Lessig, and Eugene Fiume. 2012. Fluid Simulation Using Laplacian Eigenfunctions. ACM Trans. Graph. 31, 1, Article 10 (Feb. 2012), 11 pages.

Digital Library

[7]

Sharif Elcott, Yiying Tong, Eva Kanso, Peter Schröder, and Mathieu Desbrun. 2007. Stable, Circulation-preserving, Simplicial Fluids. ACM Trans. Graph. 26, 1 (Jan. 2007).

Digital Library

[8]

Ronald Fedkiw, Jos Stam, and Henrik Wann Jensen. 2001. Visual Simulation of Smoke. In Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '01). 15--22.

Digital Library

[9]

Chuyuan Fu, Qi Guo, Theodore Gast, Chenfanfu Jiang, and Joseph Teran. 2017. A Polynomial Particle-in-cell Method. ACM Trans. Graph. 36, 6, Article 222 (Nov. 2017), 12 pages.

Digital Library

[10]

Chenfanfu Jiang, Craig Schroeder, Andrew Selle, Joseph Teran, and Alexey Stomakhin. 2015. The affine particle-in-cell method. ACM Transactions on Graphics (TOG) 34, 4 (July 2015), 51:1--51:10.

Digital Library

[11]

ByungMoon Kim, Yingjie Liu, Ignacio Llamas, and Jarek Rossignac. 2005. FlowFixer: Using BFECC for Fluid Simulation. In Proceedings of the First Eurographics Conference on Natural Phenomena (NPH'05). 51--56.

Digital Library

[12]

ByungMoon Kim, Yingjie Liu, Ignacio Llamas, and Jarek Rossignac. 2007. Advections with Significantly Reduced Dissipation and Diffusion. IEEE Transactions on Visualization and Computer Graphics 13, 1 (Jan. 2007), 135--144.

Digital Library

[13]

Doyub Kim, Oh-young Song, and Hyeong-Seok Ko. 2008. A Semi-Lagrangian CIP Fluid Solver without Dimensional Splitting. Computer Graphics Forum 27, 2 (April 2008), 467--475.

[14]

T. T. Lim and T. B. Nickels. 1992. Instability and reconnection in the head-on collision of two vortex rings. Nature 357 (1992). Issue 6375.

[15]

Chohong Min and FrÃl'dÃl'ric Gibou. 2006. A second order accurate projection method for the incompressible NavierâĂŞS-tokes equations on non-graded adaptive grids. J. Comput. Phys. 219, 2 (2006), 912 -- 929.

Digital Library

[16]

Patrick Mullen, Keenan Crane, Dmitry Pavlov, Yiying Tong, and Mathieu Desbrun. 2009. Energy-preserving Integrators for Fluid Animation. ACM Trans. Graph. 28, 3, Article 38 (July 2009), 8 pages.

Digital Library

[17]

Sang Il Park and Myoung Jun Kim. 2005. Vortex Fluid for Gaseous Phenomena. In Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA '05). 261--270.

Digital Library

[18]

André Robert. 1981. A stable numerical integration scheme for the primitive meteorological equations. Atmosphere-Ocean 19, 1 (1981), 35--46. arXiv:https://doi.org/10.1080/07055900.1981.9649098

[19]

André Robert. 1982. A Semi-Lagrangian and Semi-Implicit Numerical Integration Scheme for the Primitive Meteorological Equations. Journal of the Meteorological Society of Japan. Ser. II 60, 1 (1982), 319--325.

[20]

Destin Sandlin. 2018. Smarter Every Day: Two Vortex Rings Colliding in Slow Motion. https://www.youtube.com/watch?v=EVbdbVhzcM4. (2018).

[21]

Takahiro Sato, Christopher Batty, Takeo Igarashi, and Ryoichi Ando. 2018. Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection. Computational Visual Media 4, 3 (01 Sep 2018), 223--230.

[22]

Andrew Selle, Ronald Fedkiw, Byungmoon Kim, Yingjie Liu, and Jarek Rossignac. 2008. An Unconditionally Stable MacCormack Method. J. Sci. Comput. 35, 2-3 (June 2008), 350--371.

Digital Library

[23]

Jos Stam. 1999. Stable Fluids. In Proceedings of the 26th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '99). ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 121--128.

Digital Library

[24]

Andrew Staniforth and Jean CÃt'tÃl'. 1991. Semi-Lagrangian Integration Schemes for Atmospheric ModelsâĂŤA Review. Monthly Weather Review 119, 9 (1991), 2206--2223.

[25]

J. M. Straka, Robert B. Wilhelmson, Louis J. Wicker, John R. Anderson, and Kelvin K. Droegemeier. 1993. Numerical solutions of a nonlinear density current: A benchmark solution and comparisons. International Journal for Numerical Methods in Fluids 17, 1 (1993), 1--22. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/fld.1650170103

[26]

Steffen Weißmann and Ulrich Pinkall. 2010. Filament-based Smoke with Vortex Shedding and Variational Reconnection. ACM Trans. Graph. 29, 4 (July 2010), 115:1--115:12.

Digital Library

[27]

Dongbin Xiu and George Em Karniadakis. 2001. A Semi-Lagrangian High-Order Method for Navier--Stokes Equations. J. Comput. Phys. 172, 2 (2001), 658 -- 684.

Digital Library

[28]

Jonas Zehnder, Rahul Narain, and Bernhard Thomaszewski. 2018. An Advection-reflection Solver for Detail-preserving Fluid Simulation. ACM Trans. Graph. 37, 4, Article 85 (July 2018), 8 pages.

Digital Library

[29]

Xinxin Zhang, Robert Bridson, and Chen Greif. 2015. Restoring the Missing Vorticity in Advection-projection Fluid Solvers. ACM Trans. Graph. 34, 4 (July 2015), 52:1--52:8.

Digital Library

[30]

Yongning Zhu and Robert Bridson. 2005. Animating Sand as a Fluid. 24 (July 2005), 965--972.

Digital Library

Cited By

Zhou JChen DDeng MDeng YSun YWang SXiong SZhu B(2024)Eulerian-Lagrangian Fluid Simulation on Particle Flow MapsACM Transactions on Graphics10.1145/365818043:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658180
Sugimoto RBatty CHachisuka T(2024)Velocity-Based Monte Carlo FluidsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657405(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657405
Deng YYu HZhang DWu JZhu B(2023)Fluid Simulation on Neural Flow MapsACM Transactions on Graphics10.1145/361839242:6(1-21)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618392
Show More Cited By

Index Terms

A Second-Order Advection-Reflection Solver
1. Computing methodologies
  1. Computer graphics
    1. Animation
      1. Physical simulation

Recommendations

An advection-reflection solver for detail-preserving fluid simulation

Advection-projection methods for fluid animation are widely appreciated for their stability and efficiency. However, the projection step dissipates energy from the system, leading to artificial viscosity and suppression of small-scale details. We ...
Restoring the missing vorticity in advection-projection fluid solvers

Most visual effects fluid solvers use a time-splitting approach where velocity is first advected in the flow, then projected to be incompressible with pressure. Even if a highly accurate advection scheme is used, the self-advection step typically ...
Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

This paper analyzes the causes of the numerical errors in terms of numerical diffusion and compression arising from the use of explicit second-order total variation diminishing (TVD) schemes in one-dimensional advection simulation. It demonstrates that ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques

Proceedings of the ACM on Computer Graphics and Interactive Techniques Volume 2, Issue 2

July 2019

239 pages

EISSN:2577-6193

DOI:10.1145/3352480

Issue’s Table of Contents

Copyright © 2019 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 26 July 2019

Published in PACMCGIT Volume 2, Issue 2

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article
Research
Refereed

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
322
Total Downloads

Downloads (Last 12 months)42
Downloads (Last 6 weeks)4

Reflects downloads up to 09 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Zhou JChen DDeng MDeng YSun YWang SXiong SZhu B(2024)Eulerian-Lagrangian Fluid Simulation on Particle Flow MapsACM Transactions on Graphics10.1145/365818043:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658180
Sugimoto RBatty CHachisuka T(2024)Velocity-Based Monte Carlo FluidsACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657405(1-11)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657405
Deng YYu HZhang DWu JZhu B(2023)Fluid Simulation on Neural Flow MapsACM Transactions on Graphics10.1145/361839242:6(1-21)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618392
Nabizadeh MWang SRamamoorthi RChern A(2022)Covector fluidsACM Transactions on Graphics10.1145/3528223.353012041:4(1-16)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530120
Lesser SStomakhin ADaviet GWretborn JEdholm JLee NSchweickart EZhai XFlynn SMoffat A(2022)LokiACM Transactions on Graphics10.1145/3528223.353005841:4(1-20)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530058
Nielsen MBojsen-Hansen MStamatelos KBridson R(2022)Physics-Based Combustion SimulationACM Transactions on Graphics10.1145/352621341:5(1-21)Online publication date: 13-May-2022
https://dl.acm.org/doi/10.1145/3526213
Forootaninia ZNarain R(2020)Frequency-domain smoke guidingACM Transactions on Graphics10.1145/3414685.341784239:6(1-10)Online publication date: 27-Nov-2020
https://dl.acm.org/doi/10.1145/3414685.3417842
Ando RBatty C(2020)A practical octree liquid simulator with adaptive surface resolutionACM Transactions on Graphics10.1145/3386569.339246039:4(32:1-32:17)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392460
Huang WIseringhausen JKneiphof TQu ZJiang CHullin M(2020)Chemomechanical simulation of soap film flow on spherical bubblesACM Transactions on Graphics10.1145/3386569.339209439:4(41:1-41:13)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392094
Gagniere SHyde DMarquez-Razon AJiang CGe ZHan XGuo QTeran JLevin DKry P(2020)A hybrid lagrangian/eulerian collocated velocity advection and projection method for fluid simulationProceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation10.1111/cgf.14096(1-14)Online publication date: 6-Oct-2020
https://dl.acm.org/doi/10.1111/cgf.14096

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Article

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Issue’s Table of Contents