Geodesic
A phase-field method applied to interface tracking for blood clot formation
Applications of Mathematics, Tome 65 (2020) no. 4, pp. 447-481.

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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.
DOI : 10.21136/AM.2020.0056-19
Classification : 76D05, 76M10, 76T99
Keywords: thrombus growth; free boundary problem; fluid dynamics; phase field method; finite element method; scalability; high shear rate thrombosis 
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Čapek, Marek. A phase-field method applied to interface tracking for blood clot formation. Applications of Mathematics, Tome 65 (2020) no. 4, pp. 447-481. doi : 10.21136/AM.2020.0056-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0056-19/

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