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

by   Timo Koch, et al.

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 analyse 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.



There are no comments yet.


page 23


Projection-based resolved interface mixed-dimension method for embedded tubular network systems

We present a flexible discretization technique for computational models ...

Simulating convection-coupled phase-change in enthalpy form with mixed finite elements

Melting and solidification processes are often affected by natural conve...

An Upwind Generalized Finite Difference Method (GFDM) for Analysis of Heat and Mass Transfer in Porous Media

In this paper, an upwind meshless GFDM is presented for the first time a...

Towards HPC simulations of Billion-cell Reservoirs by Multiscale Mixed Methods

A three dimensional parallel implementation of Multiscale Mixed Methods ...

A Well-Balanced Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations

We develop a well-balanced central-upwind scheme for rotating shallow wa...

Experimental and computational comparison of freeze-thaw induced pressure generation in red and sugar maple

Sap exudation is the process whereby trees such as sugar (Acer saccharum...

Estimating a pressure dependent thermal conductivity coefficient with applications in food technology

In this paper we introduce a method to estimate a pressure dependent the...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.