Geodesic
Blood Flow Simulation Using Traceless Variant of Johnson-Segalman Viscoelastic Model
T. Bodnár1 ; M. Pires2, 3 ; J. Janela4
1 Faculty of Mechanical Engineering, Czech Technical University in Prague Karlovo Náměstí 13, 121 35 Prague 2, Czech Republic
2 Department of Mathematics and CIMA-UE, Évora University Rua Romão Ramalho, 7000-671, Évora, Portugal
3 CEMAT, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
4 Department of Mathematics and CEMAPRE, ISEG, Universidade de Lisboa Rua do Quelhas 6, 1200-781 Lisbon, Portugal
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 6, pp. 117-141.

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A traceless variant of the Johnson-Segalman viscoelastic model is presented and applied to blood flow simulations. The viscoelastic extra stress tensor is decomposed into its traceless (deviatoric) and spherical parts, leading to a reformulation of the classical Johnson-Segalman model. The equivalence of the two models is established comparing model predictions for simple test cases. The new model is validated using several 2D benchmark problems, designed to reproduce difficulties that arise in the simulation of blood flow in blood vessels or medical devices. The structure and behaviour of the new model are discussed and the future use of the new model in envisioned, both on the theoretical and numerical perspectives.
DOI : 10.1051/mmnp/20149609

T. Bodnár 1 ; M. Pires 2, 3 ; J. Janela 4

1 Faculty of Mechanical Engineering, Czech Technical University in Prague Karlovo Náměstí 13, 121 35 Prague 2, Czech Republic
2 Department of Mathematics and CIMA-UE, Évora University Rua Romão Ramalho, 7000-671, Évora, Portugal
3 CEMAT, Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
4 Department of Mathematics and CEMAPRE, ISEG, Universidade de Lisboa Rua do Quelhas 6, 1200-781 Lisbon, Portugal 
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T. Bodnár; M. Pires; J. Janela. Blood Flow Simulation Using Traceless Variant of Johnson-Segalman Viscoelastic Model. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 6, pp. 117-141. doi : 10.1051/mmnp/20149609. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149609/

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