Discretizing fluids into filaments and sheets

In many situations important for physics simulation, the relevant fields (like the vorticity of a fluid or the magnetic field of a plasma) exhibit a strong tendency to become concentrated in one-dimensional filaments or two-dimensional sheets. “Decomposing” a given continuous field into its ”constituent” filaments or sheets is important for understanding and visualizing a given field. Moreover, simulation algorithms that take into account the natural tendency of the fields to become "discretized” into filaments or sheets can be highly efficient. We also will use the methods developed in this project to reconstruct velocity fields from video capture of smoke.


  • Albert Chern and Oliver Gross.
    Force-Free Fields are Conformally Geodesic.
    preprint, December 2023.
  • Oliver Gross, Ulrich Pinkall, and Peter Schröder.
    Plasma Knots.
    Physics Letters A, August 2023.
    URL: https://www.sciencedirect.com/science/article/abs/pii/S0375960123003663.
  • Oliver Gross, Yousuf Soliman, Marcel Padilla, Felix Knöppel, Ulrich Pinkall, and Peter Schröder.
    Motion from Shape Change.
    ACM Transactions on Graphics, July 2023.
    URL: https://olligross.github.io/projects/MotionFromShapeChange/MotionFromShapeChange_project.html, doi:10.1145/3592417.
  • Patrick Schnell, Philipp Holl, and Nils Thuerey.
    Half-Inverse Gradients for Physical Deep Learning.
    International Conference on Learning Representations, March 2022.
    URL: https://arxiv.org/abs/2203.10131.
  • Steffen Wiewel, Moritz Becher, and Nils Thuerey.
    Latent-space physics: Towards learning the temporal evolution of fluid flow.
    In Computer Graphics Forum, volume 38. Wiley Online Library, 2019.
  • Albert Chern, Felix Knöppel, Franz Pedit, and Ulrich Pinkall.
    Commuting Hamiltonian flows of curves in real space forms.
    Preprint, September 2018.
    arXiv:1809.01394, dgd:493.
  • M-L Eckert, Wolfgang Heidrich, and Nils Thuerey.
    Coupled Fluid Density and Motion from Single Views.
    In Computer Graphics Forum, volume 37, 47–58. Wiley Online Library, 2018.
  • You Xie, Erik Franz, Mengyu Chu, and Nils Thuerey.
    tempogan: A temporally coherent, volumetric gan for super-resolution fluid flow.
    TOG, 37(4):95, 2018.
  • Albert Chern, Felix Knöppel, and Peter Pinkall, Ulrich and​ ​Schröder.
    Inside Fluids: Clebsch Maps for Visualization and Processing.
    ACM Trans. Graph., 36(4):142:1–142:11, July 2017.
  • Sebastian Eberhardt, Steffen Weissmann, Ulrich Pinkall, and Nils Thuerey.
    Hierarchical Vorticity Skeletons.
    Proceedings of the Symposium on Computer Animation (SCA '12), to appear:11, June 2017.
    URL: https://ge.in.tum.de/download/2017-sca-eberhardt.pdf, doi:10.1145/3099564.3099569.
  • F. Knöppel and U. Pinkall.
    Complex Line Bundles over Simplicial Complexes and their Applications.
    In A. I. Bobenko, editor, Advances in Discrete Differential Geometry. Springer, January 2017.
  • Albert Chern, Felix Knöppel, Peter Pinkall, Ulrich and​ ​Schröder, and Steffen Weißmann.
    Schrödinger's Smoke.
    ACM Trans. Graph., 35:77:1–77:13, July 2016.
  • A. Chern, U. Pinkall, and P. Schröder.
    Close-to-conformal deformations of volumes.
    ACM Transactions on Graphics, 34(4):56, 2015.
  • S. Weißmann and U. Pinkall.
    Filament-based smoke with vortex shedding and variational reconnection.
    ACM Transactions on Graphics, 2010.

  • Ulrich Pinkall and Oliver Gross.
    Differential Geometry, From Elastic Curves to Willmore Surfaces.
    Birkhäuser Cham, 2024. ISBN 978-3-031-39838-4.

PhD thesis
  • F. Knöppel.
    Complex Line Bundles over Simplicial Complexes.
    Dissertation, TU Berlin, 2015.


Prof. Dr. Ulrich Pinkall   +

Projects: A05, C07
University: TU Berlin, Institut für Mathematik, MA 822
Address: Straße des 17. Juni 136, 10623 Berlin, GERMANY
Tel: +49 30 31424607
E-Mail: pinkall[at]math.tu-berlin.de
Website: http://page.math.tu-berlin.de/~pinkall/

Prof. Dr. Nils Thuerey   +

Projects: C07
University: TU München, Inf. 15, 02.13.061
Address: Boltzmannstr. 3, 85748 Garching, GERMANY
Tel: +49 89 28919484
Fax: +49 89 28919462
E-Mail: nils.thuerey[at]tum.de
Website: https://ge.in.tum.de/about/n-thuerey/

Dr. Liwei Chen   +

Projects: C07
University: TU München, Inf. 15, 02.13.055
Address: Boltzmannstr. 3, 85748 Garching, GERMANY
Tel: +49 89 28919482
E-Mail: liwei.chen[at]tum.de
Website: https://ge.in.tum.de/about/dr-liwei-chen/

Oliver Gross   +

Projects: C07
University: TU Berlin
E-Mail: ogross[at]math.tu-berlin.de

Dr. Felix Knöppel   +

Projects: C07
University: TU Berlin
E-Mail: knoeppel[at]math.tu-berlin.de

Patrick Schnell   +

Projects: C07
University: TU München, Inf. 15, 02.13.060
Address: Boltzmannstr. 3, 85748 Garching, GERMANY
E-Mail: patrick.schnell[at]tum.de
Website: https://ge.in.tum.de/about/patrick-schnell/