SFB 1313 Publication "Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake"

January 11, 2022 /

Authors: Timo Koch, Hanchuan Wu, and Martin Schneider | Published in: Journal of Computational Physics

New SFB 1313 publication, published in Journal of Computational Physics. The paper has been prepared within SFB 1313's research project A02.

"Nonlinear mixed-dimension model for embedded tubular networks with application to root water uptake"


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.

This image shows Timo Koch

Timo Koch


Postdoctoral Researcher, SFB 1313 Associated Researcher

This image shows Hanchuan Wu

Hanchuan Wu

M. Sc.

Doctoral Researcher, Research Project A02

This image shows Martin Schneider

Martin Schneider


Principal Investigator, Research Project A02, Project INF

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