Numerical simulation of biological capsules based on interface-fitted polygonal meshes
Abstract
In this work we introduce a numerical framework for the simulation of biological capsules based on meshes that adapt iteration-wise to the shape of the membrane. The discretization leverages a Hybrid High Order method (HHO) to solve a Stokes problem with a source term distributed on the interface between the internal and the external phases. The HHO discretization supports meshes composed of general polygons, permitting to use fitted meshes that can be easily generated by cutting the elements intersected by the interface. Moreover, polygonal meshes allow arbitrarily accurate interface discretizations without introducing bulk degrees of freedom. The presentation of the simulation algorithm is completed with a proof-of-concept numerical test on a well-established benchmark: the deformation of an elastic capsule immersed in a shear flow.
Related
- Numerical reconstruction of polygonal obstacles by diffracted waves
- Numerical investigation of a homogenized model with effective interface conditions for Stokes flow through porous membranes
- Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System
- Space-Time Parallel Direct Numerical Simulation of Rayleigh-Bénard Convection
- Generating functions and efficient numerical simulation of aggregation-fragmentation kinetics
BibTeX
@misc{pietro2026numerical,
title = {{Numerical simulation of biological capsules based on interface-fitted polygonal meshes}},
author = {Daniele A. Di Pietro and Simon Mendez and Aurelio E. Spadotto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18172},
eprint = {2610.18172},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18172},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Numerical simulation of biological capsules based on interface-fitted polygonal meshes
AU - Daniele A. Di Pietro
AU - Simon Mendez
AU - Aurelio E. Spadotto
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18172
UR - https://arxiv.org/abs/2610.18172
AB - In this work we introduce a numerical framework for the simulation of biological capsules based on meshes that adapt iteration-wise to the shape of the membrane. The discretization leverages a Hybrid High Order method (HHO) to solve a Stokes problem with a source term distributed on the interface between the internal and the external phases. The HHO discretization supports meshes composed of general polygons, permitting to use fitted meshes that can be easily generated by cutting the elements intersected by the interface. Moreover, polygonal meshes allow arbitrarily accurate interface discretizations without introducing bulk degrees of freedom. The presentation of the simulation algorithm is completed with a proof-of-concept numerical test on a well-established benchmark: the deformation of an elastic capsule immersed in a shear flow.
ER -