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Dissertation
Modeling of human vitreous as viscoelastic fluid considering the orientation of collagen fibers
(2021-11)
For the most common treatment of retinal diseases worldwide by drug distribution in the human vitreous we developed the mathematical model of the vitreous. Compare to previous works we focus on the vitreous as a viscoelastic fluid including its heterogeneous property due to the orientation of collagen fibers. By using the incompressible viscoelastic Burgers-type model based on experimental data as the specific constitutive equation in the setting of continuum mechanics we considered its non-Newtonian nature. This ...
Habilitation
Numerical Methods for Fluid Flow: High Order SBP Schemes, IMEX Advection-Diffusion Splitting and Positivity Preservation for Production-Destruction PDEs
(2021-01)
The current demands regarding the numerical simulation of fluid flow often require highly accurate computations to obtain a detailed resolution of the occurring physical phenomena. The basic concept for the construction of a fluid solver is to transfer the physical model into a numerical scheme which complies with the underlying physical principles such as conservation and balances of certain quantities. In addition, the numerical methods are required to be stable and efficient. Again, stability is often determined ...