My research concerns two-phase flow in porous media, focusing on the mathematical modelling on the microscopic pore scale and upscaling to the macroscopic continuum scale as well as solving the resulting nonlinear partial differential equations on both scales. This is relevant for CO2 storage in rock, geothermal energy and oil production. Since the interface between the two phases on pore scale affects their behavior, including their flow through the porous medium on large-scale, understanding the essential processes at the pore scale is fundamental to understand the overall behavior. This work is part of the VisioFlow project.
My research on partial differential equations consists mainly of the following three topics:
- Analysis: existence and uniqueness of (weak) solutions
- Upscaling: homogenization, multiple scales, asymptotic expansions, heterogeneous media
- Numerical methods: convergence, error estimates, discretization (FEM, FVM), linearization schemes
Born on 22 January 1995 in Nürtingen, Germany
Languages: German (mother tongue), English
Since Sept. 2018: PhD studies in Mathematics at Hasselt University, Belgium
Oct. 2016 – Sept. 2018: Double MSc Degree
Master of Science in Simulation Technology at the University of Stuttgart, Germany (graduated "mit Auszeichnung")
Industrial and Applied Mathematics at the Eindhoven University of Technology, The Netherlands (graduated "cum laude")
Oct. 2013 – Nov. 2016: Bachelor of Science in Simulation Technology at the University of Stuttgart, Germany
Sept. 2011 – Sept. 2013: Early Studies in Mathematics at the University of Stuttgart, Germany
Oct. 2016 – Aug. 2017: Student assistant for research at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany
Oct. 2014 – Sept. 2016: Student assistant for tutorials in the modules Analysis 1 – 3 and Numerical Linear Algebra at the University of Stuttgart, Germany
Oct. 2017 – June 2018: Scholarship of the Baden-Württemberg Stiftung
Dec. 2013 – Sept. 2018: Scholarship of the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes e.V.)
Oct. 2013 – Mar. 2014: Germany Scholarship of the University of Stuttgart
Refereed journal publications:
- On an averaged model for immiscible two-phase flow with surface tension and dynamic contact angle in a thin strip, Stud. Appl. Math. (2021, Early View), with C. Bringedal and I.S. Pop (see also CMAT Report UP-20-06).
- Linearized domain decomposition methods for two-phase porous media flow models involving dynamic capillarity and hysteresis, Comput. Methods Appl. Mech. Eng. Vol 372 (2020), 113364, with I.S. Pop, B. Koren (see also CMAT Report UP-20-03).
Book contributions and proceedings:
- A Linear Domain Decomposition Method for Non-Equilibrium Two-Phase Flow Models, in Numerical Mathematics and Advanced Applications - ENUMATH 2019, Lecture Notes in Computational Science and Engineering, Vol. 139, Springer International, 2021, pp. 145-153, with I.S. Pop, B. Koren (see also CMAT Report UP-19-14, Hasselt University).
CMAT Reports (Hasselt University):
- M.J. Gander, S.B. Lunowa, C. Rohde, Non-overlapping Schwarz waveform-relaxation for nonlinear advection-diffusion equations, CMAT Report UP-21-03, Hasselt University.
Linearization and Domain Decomposition Methods for Two-Phase Flow in Porous Media, Master thesis, Eindhoven University of Technology, Department of Mathematics and Computer Science, The Netherlands, 2018.
Hasselt University, CMAT Reports
- Consistent and asymptotic-preserving finite-volume domain decomposition methods for singularly perturbed elliptic equations, CMAT Report UP-21-02, with M.J. Gander and C. Rohde