Back to Search
Start Over
Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles
- Source :
- Journal of Computational Physics, Journal of Computational Physics, Elsevier, 2021, 436, pp.110288. ⟨10.1016/j.jcp.2021.110288⟩, Journal of Computational Physics, 2021, 436, pp.110288. ⟨10.1016/j.jcp.2021.110288⟩
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus.
- Subjects :
- Volume and area preserving
Vol- ume and area preserving
Diffusion generated motion
Physics and Astronomy (miscellaneous)
Computer science
Interface (Java)
and phrases: Diffusion generated motion
Signed distance function
Clifford torus
010103 numerical & computational mathematics
Willmore flow
01 natural sciences
Level set
Dimension (vector space)
FOS: Mathematics
Applied mathematics
Mathematics - Numerical Analysis
[PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph]
0101 mathematics
Diffusion (business)
[MATH]Mathematics [math]
High-order geometrical flow
Numerical Analysis
Level set (data structures)
Applied Mathematics
Numerical Analysis (math.NA)
Thresholding
Computer Science Applications
010101 applied mathematics
Computational Mathematics
Flow (mathematics)
Modeling and Simulation
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Subjects
Details
- Language :
- English
- ISSN :
- 00219991 and 10902716
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics, Journal of Computational Physics, Elsevier, 2021, 436, pp.110288. ⟨10.1016/j.jcp.2021.110288⟩, Journal of Computational Physics, 2021, 436, pp.110288. ⟨10.1016/j.jcp.2021.110288⟩
- Accession number :
- edsair.doi.dedup.....d7a1ee96f0e30e29dbb834327001dd50