A phase-field method applied to interface tracking for blood clot formation

Marek Čapek

Applications of Mathematics (2020)

  • Volume: 65, Issue: 4, page 447-481
  • ISSN: 0862-7940

Abstract

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The high shear rate thrombus formation was only recently recognized as another way of thrombosis. Models proposed in Weller (2008), (2010) take into account this type of thrombosis. This work uses the phase-field method to model these evolving interface problems. A loosely coupled iterative procedure is introduced to solve the coupled system of equations. Convergence behavior on two levels of refinement of perfusion chamber geometry and cylinder geometry is then studied. The perfusion chamber simulations show good agreement with the original results of Weller. The code is implemented in FEM-library deal.ii Alzeta et al. (2018), which enables distribution of computations to large number of processing units. A scalability and numerical performance study of the loosely coupled iterative procedure is performed, combined with several preconditioners for the linear subproblems.

How to cite

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Čapek, Marek. "A phase-field method applied to interface tracking for blood clot formation." Applications of Mathematics 65.4 (2020): 447-481. <http://eudml.org/doc/297329>.

@article{Čapek2020,
abstract = {The high shear rate thrombus formation was only recently recognized as another way of thrombosis. Models proposed in Weller (2008), (2010) take into account this type of thrombosis. This work uses the phase-field method to model these evolving interface problems. A loosely coupled iterative procedure is introduced to solve the coupled system of equations. Convergence behavior on two levels of refinement of perfusion chamber geometry and cylinder geometry is then studied. The perfusion chamber simulations show good agreement with the original results of Weller. The code is implemented in FEM-library deal.ii Alzeta et al. (2018), which enables distribution of computations to large number of processing units. A scalability and numerical performance study of the loosely coupled iterative procedure is performed, combined with several preconditioners for the linear subproblems.},
author = {Čapek, Marek},
journal = {Applications of Mathematics},
keywords = {thrombus growth; free boundary problem; fluid dynamics; phase field method; finite element method; scalability; high shear rate thrombosis},
language = {eng},
number = {4},
pages = {447-481},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A phase-field method applied to interface tracking for blood clot formation},
url = {http://eudml.org/doc/297329},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Čapek, Marek
TI - A phase-field method applied to interface tracking for blood clot formation
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 447
EP - 481
AB - The high shear rate thrombus formation was only recently recognized as another way of thrombosis. Models proposed in Weller (2008), (2010) take into account this type of thrombosis. This work uses the phase-field method to model these evolving interface problems. A loosely coupled iterative procedure is introduced to solve the coupled system of equations. Convergence behavior on two levels of refinement of perfusion chamber geometry and cylinder geometry is then studied. The perfusion chamber simulations show good agreement with the original results of Weller. The code is implemented in FEM-library deal.ii Alzeta et al. (2018), which enables distribution of computations to large number of processing units. A scalability and numerical performance study of the loosely coupled iterative procedure is performed, combined with several preconditioners for the linear subproblems.
LA - eng
KW - thrombus growth; free boundary problem; fluid dynamics; phase field method; finite element method; scalability; high shear rate thrombosis
UR - http://eudml.org/doc/297329
ER -

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