Page 509 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 509
MULTISCALE MODELING AND METHODS: APPLICATION IN ENGINEERING,
BIOLOGY AND MEDICINE (MS-80)
More details about the kernels will be discussed in the talk by Éric Canon: On weakly
singular kernels arising in equations set on a graph, modelling a flow in a networtk of thin
tubes.
References
[1] Panasenko G. P., Pileckas K., Flows in a tube structure: equation on the graph, Journal of
Mathematical Physics, Vol 55: 081505, 2014.
Robust parameter estimation in fluid flow models from velocity
measurements
Jeremias Garay, j.e.garay.labra@rug.nl
University of Groningen, Netherlands
Coauthor: Cristobal Bertoglio
Parameter estimation in blood flow models from measured velocity data is a key step for patient-
specific hemodynamic analysis. However, the quality of the estimation can be compromised if
the measurements suffer from high noise levels and aliasing artifacts, which usually affect this
type of acquisitions. Moreover, due to the change in the parameter values during the parameter
optimization process, efficient and robust forward solvers – unconditionally stable – are also
needed.
The aim of this work is hence twofold. Firstly, we propose an easy-to-implement, uncondi-
tionally stable fractional step solver for a multiscale 3D-0D coupled flow problem, with which
we can formulate non-linear Kalman filtering strategy. Secondly, we propose as adaptation a
new inverse problem being able to tackle aliased and noisy velocity measurements.
Time periodic Navier-Stokes equations in a thin tube structures motivated
by hemodynamic
Rita Juodagalvyte˙, rita.juodagalvyte@mif.vu.lt
Vilnius University, Lithuania
Coauthors: Konstantinas Pileckas, Grigory Panasenko
The time-periodic Navier-Stokes equations are considered in thin tube structures in three and
two-dimensional settings with Dirichlet boundary conditions. A thin tube structure is defined
as finite union of thin cylinders which are characterized by a small parameter ε which is the
ratio of the height and the diameter of the cylinders. We consider the case of the finite or big
coefficient before the time derivative. This setting is motivated by hemodynamic (small vessels).
Theorems of existence and uniqueness of a solution are proved. Complete asymptotic expansion
of a solution is constructed and justified. The method of asymptotic partial decomposition of
the domain is justified for the time-periodic problem. The conductivity problem on the graph
is solving using numerical methods. The numerical results are obtained in collaboration with
Frédéric Chardard.
R. Juodagalvyte˙ was supported by the LABEX MILYON (ANR-10-LABX-0070) of Uni-
veristé de Lyon within the program "Investiments d’Avenir" (ANR-11-IDEX-0007) operated by
the French National Research Agency.
507
BIOLOGY AND MEDICINE (MS-80)
More details about the kernels will be discussed in the talk by Éric Canon: On weakly
singular kernels arising in equations set on a graph, modelling a flow in a networtk of thin
tubes.
References
[1] Panasenko G. P., Pileckas K., Flows in a tube structure: equation on the graph, Journal of
Mathematical Physics, Vol 55: 081505, 2014.
Robust parameter estimation in fluid flow models from velocity
measurements
Jeremias Garay, j.e.garay.labra@rug.nl
University of Groningen, Netherlands
Coauthor: Cristobal Bertoglio
Parameter estimation in blood flow models from measured velocity data is a key step for patient-
specific hemodynamic analysis. However, the quality of the estimation can be compromised if
the measurements suffer from high noise levels and aliasing artifacts, which usually affect this
type of acquisitions. Moreover, due to the change in the parameter values during the parameter
optimization process, efficient and robust forward solvers – unconditionally stable – are also
needed.
The aim of this work is hence twofold. Firstly, we propose an easy-to-implement, uncondi-
tionally stable fractional step solver for a multiscale 3D-0D coupled flow problem, with which
we can formulate non-linear Kalman filtering strategy. Secondly, we propose as adaptation a
new inverse problem being able to tackle aliased and noisy velocity measurements.
Time periodic Navier-Stokes equations in a thin tube structures motivated
by hemodynamic
Rita Juodagalvyte˙, rita.juodagalvyte@mif.vu.lt
Vilnius University, Lithuania
Coauthors: Konstantinas Pileckas, Grigory Panasenko
The time-periodic Navier-Stokes equations are considered in thin tube structures in three and
two-dimensional settings with Dirichlet boundary conditions. A thin tube structure is defined
as finite union of thin cylinders which are characterized by a small parameter ε which is the
ratio of the height and the diameter of the cylinders. We consider the case of the finite or big
coefficient before the time derivative. This setting is motivated by hemodynamic (small vessels).
Theorems of existence and uniqueness of a solution are proved. Complete asymptotic expansion
of a solution is constructed and justified. The method of asymptotic partial decomposition of
the domain is justified for the time-periodic problem. The conductivity problem on the graph
is solving using numerical methods. The numerical results are obtained in collaboration with
Frédéric Chardard.
R. Juodagalvyte˙ was supported by the LABEX MILYON (ANR-10-LABX-0070) of Uni-
veristé de Lyon within the program "Investiments d’Avenir" (ANR-11-IDEX-0007) operated by
the French National Research Agency.
507
