# Transportation-based Visualization of Energy Conversion

### Oliver Fernandes, Steffen Frey, Thomas Ertl

#### Abstract

We present a novel technique to visualize the transport of and conversion between internal and kinetic energy in compressible flow data. While the distribution of energy can be directly derived from flow state variables (e.g., velocity, pressure and temperature) for each time step individually, there is no information regarding the involved transportation and conversion processes. To visualize these, we model the energy transportation problem as a graph that can be solved by a minimum cost flow algorithm, inherently respecting energy conservation. In doing this, we explicitly consider various simulation parameters like boundary conditions and energy transport mechanisms. Based on the resulting flux, we then derive a local measure for the conversion between energy forms using the distribution of internal and kinetic energy. To examine this data, we employ different visual mapping techniques that are specifically targeted towards different research questions. In particular, we introduce glyphs for visualizing local energy transport, which we place adaptively based on conversion rates to mitigate issues due to clutter and occlusion. We finally evaluate our approach by means of data sets from different simulation codes and feedback by a domain scientist.

#### References

- Bonneel, N., van de Panne, M., Paris, S., and Heidrich, W. (2011). Displacement interpolation using lagrangian mass transport. ACM Trans. Graph., 30(6):158:1- 158:12.
- Borgo, R., Kehrer, J., Chung, D. H. S., Maguire, E., Laramee, R. S., Hauser, H., Ward, M., and Chen, M. (2013). Glyph-based visualization: Foundations, design guidelines, techniques and applications. Eurographics Association.
- Boring, E. and Pang, A. (1996). Directional flow visualization of vector fields. In Visualization 7896. Proceedings., pages 389-392.
- Goedbloed, J. and Poedts, S. (2004). Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press.
- Goldberg, A. V. and Tarjan, R. E. (1986). A new approach to the maximum flow problem. In Proceedings of ACM Symposium on Theory of Computing, STOC 7886, pages 136-146, New York, NY, USA. ACM.
- Goldberg, A. V. and Tarjan, R. E. (1990). Finding minimum-cost circulations by successive approximation. Math. Oper. Res., 15(3):430-466.
- Hasert, M. (2014). Multi-scale Lattice Boltzmann simulations on distributed octrees; 1. Aufl. PhD thesis, M ünchen.
- Hlawatsch, M., Leube, P., Nowak, W., and Weiskopf, D. (2011). Flow radar glyphs-static visualization of unsteady flow with uncertainty. IEEE TVCG, 17(12):1949-1958.
- Kraus, M. and Ertl, T. (2001). Interactive data exploration with customized glyphs. In WSCG, pages 20-23.
- Kroes, T., Post, F. H., and Botha, C. P. (2011). Interactive direct volume rendering with physically-based lighting. techreport 2011-11, TU Delft. 1-10.
- Landau, L. D. and Lifshitz, E. M. (1987). Fluid Mechanics, Second Edition. Butterworth-Heinemann, 2 edition.
- Laramee, R. S., Schneider, J., and Hauser, H. (2004). Texture-based flow visualization on isosurfaces from computational fluid dynamics. In IEEE TVCG / VisSym, pages 85-90.
- Leal, L. G. (2007). Advanced transport phenomena: fluid mechanics and convective transport processes. Cambridge University Press.
- McLoughlin, T., Jones, M. W., Laramee, R. S., Malki, R., Masters, I., and Hansen, C. D. (2013). Similarity measures for enhancing interactive streamline seeding. IEEE TVCG, 19(8):1342-1353.
- McLoughlin, T., Laramee, R. S., Peikert, R., Post, F. H., and Chen, M. (2010). Over two decades of integrationbased, geometric flow visualization. Computer Graphics Forum, 29(6):1807-1829.
- Meyers, J. and Meneveau, C. (2012). Flow visualization using momentum and energy transport tubes and applications to turbulent flow in wind farms. J. Fluid Mech. (2013), vol. 715, pp. 335-358.
- Ropinski, T., Oeltze, S., and Preim, B. (2011). Survey of Glyph-based Visualization Techniques for Spatial Multivariate Medical Data. Computers & Graphics.
- Rubner, Y., Tomasi, C., and Guibas, L. (2000). The earth mover's distance as a metric for image retrieval. International Journal of Computer Vision, 40(2):99-121.
- Sadlo, F., Üffinger, M., Pagot, C., Osmari, D., Comba, J., Ertl, T., Munz, C.-D., and Weiskopf, D. (2011). Visualization of cell-based higher-order fields. Computing in Science and Engineering, 13(3):84-91.
- Sankey, H. R. (1905). The energy chart : practical applications to reciprocating steam-engines. Albert Frost and Sons.
- Schroeder, W. J., Volpe, C. R., and Lorensen, W. E. (1991). The stream polygon-a technique for 3d vector field visualization. In IEEE Conference on Visualization, pages 126-132, 417.
- Schultz, T. and Kindlmann, G. (2010). A maximum enhancing higher-order tensor glyph. Computer Graphics Forum, 29(3):1143-1152.
- Tong, X., Zhang, H., Jacobsen, C., Shen, H.-W., and McCormick, P. (2016). Crystal Glyph: Visualization of Directional Distributions Based on the Cube Map. In EuroVis 2016 - Short Papers.
- Üffinger, M., Schweitzer, M. A., Sadlo, F., and Ertl, T. (2011). Direct visualization of particle-partition of unity data. In Proceedings of VMV, pages 255-262.
- Wittenbrink, C. M., Pang, A. T., and Lodha, S. K. (1996). Glyphs for visualizing uncertainty in vector fields. IEEE TVCG, 2(3):266-279.

#### Paper Citation

#### in Harvard Style

Fernandes O., Frey S. and Ertl T. (2017). **Transportation-based Visualization of Energy Conversion** . In *Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)* ISBN 978-989-758-228-8, pages 52-63. DOI: 10.5220/0006098200520063

#### in Bibtex Style

@conference{ivapp17,

author={Oliver Fernandes and Steffen Frey and Thomas Ertl},

title={Transportation-based Visualization of Energy Conversion},

booktitle={Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)},

year={2017},

pages={52-63},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006098200520063},

isbn={978-989-758-228-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: IVAPP, (VISIGRAPP 2017)

TI - Transportation-based Visualization of Energy Conversion

SN - 978-989-758-228-8

AU - Fernandes O.

AU - Frey S.

AU - Ertl T.

PY - 2017

SP - 52

EP - 63

DO - 10.5220/0006098200520063