Geodesic
Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries
Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 166-180 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present a method for calculating the signed distance field to three-dimensional geometric models by representing them as a result of Boolean operations on elementary objects for each of which the signed distance is known. Two versions of the algorithm are proposed. The first is a simplified version for quick calculation of the rough distance approximation (with an exact zero isosurface and correct separation of domains inside and outside the model). The second version includes calculation of the distance to the intersection contours between elements, allowing the distance to be reconstructed with a greater accuracy without considerable additional computational costs. Both methods are much faster than the computation of distance based on the triangulation of the surfaces. The proposed approach also allows for interactively changing relative positions and orientation of the geometry parts; this makes it possible to perform calculations with moving boundaries. The approach has been tested in fluid dynamics simulation with an interphase boundary and adaptive multilevel grid refinement in Basilisk open source code for simulation of multiphase flows.
Mots-clés : distance to object
Keywords: computational geometry, numerical modeling, continuous medium, dynamic grid. 
@article{SJIM_2024_27_4_a10,
     author = {M. Y. Hrebtov and R. I. Mullyadzhanov},
     title = {Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {166--180},
     year = {2024},
     volume = {27},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2024_27_4_a10/}
}
TY  - JOUR
AU  - M. Y. Hrebtov
AU  - R. I. Mullyadzhanov
TI  - Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2024
SP  - 166
EP  - 180
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJIM_2024_27_4_a10/
LA  - ru
ID  - SJIM_2024_27_4_a10
ER  - 
%0 Journal Article
%A M. Y. Hrebtov
%A R. I. Mullyadzhanov
%T Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2024
%P 166-180
%V 27
%N 4
%U http://geodesic.mathdoc.fr/item/SJIM_2024_27_4_a10/
%G ru
%F SJIM_2024_27_4_a10
M. Y. Hrebtov; R. I. Mullyadzhanov. Computation of a distance field by means of combined geometry representation in fluid dynamics simulations with embedded boundaries. Sibirskij žurnal industrialʹnoj matematiki, Tome 27 (2024) no. 4, pp. 166-180. http://geodesic.mathdoc.fr/item/SJIM_2024_27_4_a10/

[1] Popinet S., “A quadtree-adaptive multigrid solver for the Serre—Green—Naghdi equations”, J. Comput. Phys., 302:2 (2015), 336–358 | DOI

[2] Popinet S., “An accurate adaptive solver for surface-tension-driven interfacial flows”, J. Comput. Phys., 228:16 (2009), 5838–5866 | DOI

[3] Van Hooft J. A., Popinet S., Van Heerwaarden C. C., Van der Linden S. J., De Roode S. R., Van de Wiel B. J., “Towards adaptive grids for atmospheric boundary-layer simulations”, Boundary Layer Meteorol., 167:3 (2018), 421–443 | DOI

[4] Almgren A. S., Bell J. B., Colella P., Howell L. H., Welcome M. L., “A conservative adaptive projection method for the variable density incompressible Navier—Stokes equations”, J. Comput. Phys., 142:1 (1998), 1–46 | DOI

[5] Greaves D., “A quadtree adaptive method for simulating fluid flows with moving interfaces”, J. Comput. Phys., 194:1 (2004), 35–56 | DOI

[6] Huet D. P., Wachs A., “A Cartesian-octree adaptive front-tracking solver for immersed biological capsules in large complex domains”, J. Comput. Phys., 492:1 (2023), 112424 | DOI

[7] Johansen H., Colella P., “A Cartesian grid embedded boundary method for Poisson's equation on irregular domains”, J. Comput. Phys., 147:1 (1998), 60–85 | DOI

[8] Menter F. R., “Two-equation eddy-viscosity turbulence models for engineering application”, AIAA J., 32:8 (1994), 1598–1605 | DOI

[9] Günther C., Meinke M., Schröder W., “A flexible level-set approach for tracking multiple interacting interfaces in embedded boundary methods”, Comput. Fluids, 102:1 (2014), 182–202 | DOI

[10] Limare A., Popinet S., Josserand C., Xue Z., Ghigo A., “A hybrid level-set/embedded boundary method applied to solidification-melt problems”, J. Comput. Phys., 474:10 (2023), 111829 | DOI

[11] Cheny Y., Botella O., “The LS-STAG method: A new immersed boundary/level-set method for the computation of incompressible viscous flows in complex moving geometries with good conservation properties”, J. Comput. Phys., 229:4 (2010), 1043–1076 | DOI

[12] Jones M. W., Baerentzen J. A., Sramek M., “3D distance fields: A survey of techniques and applications”, IEEE Trans. Vis. Comput. Graph., 12:4 (2006), 581–599 | DOI

[13] Hormann K., Agathos A., “The point in polygon problem for arbitrary polygons”, Comput. Geom., 20:3 (2001), 1043–1076 | DOI

[14] Baerentzen J. A., Aanaes H, “Signed distance computation using the angle weighted pseudonormal”, IEEE Trans. Vis. Comput. Graph., 11:3 (2005), 243–253 | DOI

[15] Vozhakov I. S., Hrebtov M. Y., Yavorsky N. I., Mullyadzhanov R. I., “Numerical Simulations of Swirling Water Jet Atomization: A Mesh Convergence Study”, Water, 15:14 (2023), 2552 | DOI

[16] Jones M. W., 3D distance from a point to a triangle, Technical Report CSR-5, Department of Computer Science, University of Wales Swansea, 1995