| Issue |
ESAIM: M2AN
Volume 58, Number 5, September-October 2024
|
|
|---|---|---|
| Page(s) | 1681 - 1724 | |
| DOI | https://doi.org/10.1051/m2an/2024060 | |
| Published online | 23 September 2024 | |
The modelling error in multi-dimensional time-dependent solute transport models
Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Kristian Augusts Gate 23, 0164 Oslo, Norway
* Corresponding author: rami@simula.no
Received:
12
May
2023
Accepted:
14
July
2024
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are widely applicable for modelling transport in vascularized tissue, brain perivascular spaces, vascular plants and similar environments. We show the existence and uniqueness of solutions to both the full- and the multi-dimensional equations under suitable assumptions on the domain velocity. Moreover, we quantify the associated modelling errors by establishing a-priori estimates in evolving Bochner spaces. In particular, we show that the modelling error decreases with the characteristic vessel diameter and thus vanishes for infinitely slender vessels. Numerical tests in idealized geometries corroborate and extend upon our theoretical findings.
Mathematics Subject Classification: 35K45 / 65G99 / 65J08 / 65M15 / 92-10
Key words: Multi-dimensional modeling / time dependent convection–diffusion / solute transport models / modeling error in evolving Bochner spaces
© The authors. Published by EDP Sciences, SMAI 2024
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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