Speaker: **Karel Tůma**

Title: **Thermomechanical viscoelastic rate-type models with temperature dependent material coefficients**

Abstract: Response of many real materials such as asphalt, melted glass or rubber changes significantly with temperature. A frequently used approach of dealing with a model with complicated rheology/response is to take the governing equations describing the mechanical part, make the material parameters temperature dependent and add a classical heat equation with Newtonian dissipation. However, such evolution equation for temperature is not consistent with the mechanical part. Since all above metioned material can be reasonably described by viscoelastic fluid/solid models, we derive thermodynamically compatible viscoelastic rate-type models with temperature dependent material coefficients and couple the system with a consistent evolution equation for temperature. The coupled thermomechanical models are tested in two simulations: oscilating deformation of a rectangular plate with a circular hole; and deformation of a cracked material. In both cases the growth of the temperature close to the hole in the material is observed.

Speaker: **Helena Švihlová**

Title: **Interpretation of the magnetic resonance data and their use in computational fluid dynamics**

Abstract: The aortic valve stenosis and its pathological severity can be evaluated through the pressure difference in the aortic root. This can be computed from the velocity measured non-invasively by Doppler echocardiography or magnetic resonance imaging. The new methods in magnetic resonance imaging (4D PC-MRI) allow the use of data-driven methods.

In this contribution, we will focus more on the physiological flow in the aortic root and aorta and the slip mechanism acting on the boundary. We will show the impact of the chosen wall boundary conditions to the vortex formation in the aortic root. Finally, we will present the velocity data obtained from 4D PC-MRI and we will discuss their validity.

Speaker: **Michal Bathory**

Title: **Existence analysis of rate-type viscoelastic fluids with stress diffusion**

Abstract: In the talk, we will first recall some standard models for unsteady flows of incompressible viscoelastic fluids, such as the Navier-Stokes coupled with Oldroyd-B or Giesekus models. Then, we will discuss the main difficulties that arise when one tries to prove an existence of a weak solution for such models. And finally, we show how to get around these difficulties by strengthening of the dissipation, or of the energy storage mechanism.

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*Speaker*: **Helena Švihlová and Jaroslav Hron**

*Title*: **Computational study of hemodynamical flow in cerebral aneurysms and common carotid artery**

*Abstract*: We will give overview of two hemodynamical flow problems, namely the flow in cerebral aneurysm and flow in common carotid artery, where the medical community can benefit from the knowledge of the flow fields. In both cases it is well well established that hemodynamics has a significant role in possible further evolution of unphysiological conditions, like growth or rupture of the aneurysm or growth or deposit of a plaque in the carotid artery.

We will present assumptions and limitations of the models used in CFD computations as well as the potential benefits in a clinical practice in a near future. We will discuss the limitations at different levels of the blood flow modeling and our experience with setup of computational methods using academic open source computational tools (PETSc, FEniCS, VMTK).

We will describe certain intermediate steps like image segmentation and boundary condition extraction as well as extension of the models to non-newtonian behavior of the blood and possible vessel wall interactions. We will briefly discuss the numerical methods in context of high performance computing.

In this second part of the seminar Klára Kalousová, Kathryn Lund, Malte Kampschulte and Giovanni Gravina will give a talk.

For more details see: http://mathmac.cuni.cz/2018-2023/wp-content/uploads/2019/11/UNCE_MathMAC-Seminar_2019-11-1.pdf

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The first part of junior researchers will present their works. The next two seminars (December 2 and December 9) will consist of the other talks. For more details see: http://mathmac.cuni.cz/2018-2023/wp-content/uploads/2019/11/UNCE_MathMAC-Seminar_2019-11-1.pdf