People
Prof. Taras Mel'nyk
Duration
July 2023 - December 2023
Research
About this project
Hybrid-dimensional models are frequently used to model fluid flow in fractured porous media. A critical issue for understanding flow in debris-filled fractures by lower-dimensional models is the handling of bifurcating network geometries. In this project we focus on the development of models for the flow through junctions in tubular networks. The models will be derived on the REV scale from fully-dimensional mathematical models using tools from asymptotic analysis. We will start from simple transport equations for the flow, reaching out to strongly nonlinear two-phase flow. Based on preliminary work on (semi)linear evolution equation it is aimed to verify the asymptotic limit models rigorously in simplified situations. The project includes a numerical study (jointly with B03-Rohde) that could provide simulation data that can be compared to experimental data from Z02-Karadimitriou/Steeb.
Publications
- Mel’nyk, T. A., & Durante, T. (2024). Spectral problems with perturbed Steklov conditions in thick junctions with branched structure. Applicable Analysis, 1–26. https://doi.org/10.1080/00036811.2024.2322644
- Mel’nyk, T., & Rohde, C. (2024). Asymptotic expansion for convection-dominated transport in a thin graph-like junction. Analysis and Applications, 22(05), Article 05. https://doi.org/10.1142/s0219530524500040
- Mel’nyk, T. A., & Rohde, C. (2024). Asymptotic approximations for semilinear parabolic convection-dominated transport problems in thin graph-like networks. Journal of Mathematical Analysis and Applications, 529(1), Article 1. https://doi.org/10.1016/j.jmaa.2023.127587
- Mel’nyk, T., & Rohde, C. (2024). Puiseux asymptotic expansions for convection-dominated transport problems in thin graph-like networks: Strong boundary interactions. Asymptotic Analysis, 137(1–2), Article 1–2. https://doi.org/10.3233/asy-231876
Contact
Christian Rohde
Prof. Dr. rer. nat.Deputy Spokesperson, Principal Investigator, Research Projects B03 and C02, Project MGK