- Timo Koch (University of Olso, SFB 1313 associated researcher)
- Hanchuan Wu (University of Stuttgart, SFB 1313 Research Project A02)
- Martin Schneider (University of Stuttgart, SFB 1313 Research Projects INF and A02)
We present a numerical scheme for the solution of nonlinear mixed-dimensional PDEs describing coupled processes in embedded tubular network system in exchange with a bulk domain. Such problems arise in various biological and technical applications such as in the modeling of root-water uptake, heat exchangers, or geothermal wells. The nonlinearity appears in form of solution-dependent parameters such as pressure-dependent permeability or temperature-dependent thermal conductivity. We derive and analyze a numerical scheme based on distributing the bulk-network coupling source term by a smoothing kernel with local support. By the use of local analytical solutions, interface unknowns and fluxes at the bulk-network interface can be accurately reconstructed from coarsely resolved numerical solutions in the bulk domain. Numerical examples give confidence in the robustness of the method and show the results in comparison to previously published methods. The new method outperforms these existing methods in accuracy and efficiency. In a root water uptake scenario, we accurately estimate the transpiration rate using only a few thousand 3D mesh cells and a structured cube grid whereas other state-of-the-art numerical schemes require millions of cells and local grid refinement to reach comparable accuracy.
- SFB 1313 Publication "Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake"
- SFB 1313 research project A02 "Advanced modelling concepts for coupling free flow with porous-media flow"