Research Project D02

Parallel numerical coupling methods for interface problems


Miriam Schulte

Alexander Jaust (Former principal investigator in 2022)

Jun Chen

Alexander Jaust (Former post-doctoral researcher from 2018 to 2021)


Data sets published by project D02 can be found on the DaRUS website

Publications in scientific journals

  1. Conference papers

    1. Jaust, A., Weishaupt, K., Mehl, M., & Flemisch, B. (2020). Partitioned Coupling Schemes for Free-Flow and Porous-Media Applications with Sharp Interfaces. In R. Klöfkorn, E. Keilegavlen, F. A. Radu, & J. Fuhrmann (Eds.), Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (pp. 605--613). Springer International Publishing.
  2. (Journal-) Articles

    1. Bringedal, C., & Jaust, A. (2024). Phase-field modeling and effective simulation of non-isothermal reactive transport. Results in Applied Mathematics, 21, 100436.
    2. Schmidt, P., Jaust, A., Steeb, H., & Schulte, M. (2022). Simulation of flow in deformable fractures using a quasi-Newton based partitioned coupling approach. Computational Geosciences.
    3. Rodenberg, B., Desai, I., Hertrich, R., Jaust, A., & Uekermann, B. (2021). FEniCS–preCICE: Coupling FEniCS to other simulation software. SoftwareX, 16, 100807.


About this Project

Many interesting applications are multiphysics problems which are coupled via a sharp interface. Examples for this are coupled free and porous-medium flow or the hydromechanical coupling between a fluid filled fractures and the surrounding porous matrix. In our project, we tackle such problems by a partitioned coupling approach that is based on the idea of domain decomposition. We interpret each subdomain as individual problem with its own solver/software that is coupled to the other problems based on suitable coupling conditions and the respective data exchange. This is realized by using our open-source library preCICE which takes care of data communication, stabilisation of the coupling and coupling steering.

Sketch of the coupling approach using preCICE. The coupling is steered by preCICE and data are communicated and mapped between different solvers. This allows to coupled DuMuX, e.g., with other solvers.


We have focused on three main applications: (i) coupling free and porous-media flows, (ii) hydromechanical coupled problems for fracture opening, and (iii) the use of preCICE and its data-mapping facilities for visualization purposes. The coupling of free and porous-media flows has been achieved using standard coupling conditions, such as the Beavers-Joseph(-Saffman) coupling condition, and the solvers provided by DuMuX in cooperation with A02 and the in-house solver of project A03. Our experiments have shown that the partitioned coupling approach works well for the considered problems if the coupling directions, i.e., the direction coupling conditions are applied and data are exchanged, is chosen carefully. More experiments have to be done for highly parallel simulations in 3D. The evaluation of the new coupling conditions developed in project A03 is currently work in progress.

Model setup of free flow passing a porous medium. Results obtained from the partitioned couping using DuMuX in both domains are presented in two and three space dimensions.

Simulating the hydromechanical coupling of high-aspect ratio fractures and the surrounding porous medium has been special as the model is mixed-dimensional, i.e., the fracture hydrodynamics is modelled in 2D while the surrounding porous matrix is modelled in 3D. Thus, new ways of mapping data and data exchange between the subdomains were  studied. This led to a prototype implementation of new data agglomoration techniques within preCICE to ensure both good stability and full parallelisation. Together with project B05, we implemented solvers and investigated different stabilization schemes to obtain a fully parallelised implementation of the mixed-dimensional model.

Example of a threedimensional porous matrix with an embedded two-dimensional fracture (disc, highlighted in red). The porous matrix has ben cut open for better visibility 2 and to show parts of the computational mesh. The colours in the porous matrix indicate deformation (largest at the fracture), the colours in the fracture indicate the pressure.

Visualization and visual comparison of (simulation) data is not straight-forward due to different meshes and discretizations techniques used. Therefore, we collaborated with projects D01 and D03 to investigate a black-box visualization approach which would use the data-mapping capabilities of preCICE to represent arbitrary data on a defined reference mesh for better and easier comparison.

Bildunterschrift: Sketch of the visualization approach. The data from any mesh, e.g., mesh A or mesh B, are mapped by preCICE onto the reference mesh for visualization.
Bildunterschrift: Sample visualization using the visualization software inpreCICE which was developed together with projects D01 and D03.

Future Work

Upcoming work with A02 and A03 will build on the current results for flow coupling in porous media applications with a focus on the new coupling conditions and massively parallel computations in three space dimensions. Together with B05, we want to devise further stabilization, data mapping and startup procedures to tackle more challenging hydromechanical coupling simulations, expecially for fracture networks. The visualization approach will be generalised in cooperation with D01 and D03.

Besides the interface-coupled problems, volume-coupled problems play a major role within the CRC. Therefore, we plan to extend the capabilities of preCICE for adaptive micro-macro coupling applications with focus on the applications as they appear, for example, in A05. This will be based on the work of project PN5-9 “Adaptive and flexible macro-micro coupling software” within DFG-EXC 2075 “Data-Integrated Simulation Science (SimTech)” by Benjamin Uekermann.

Other projects using preCICE

preCICE is being used nationally and internationally in many projects, that contribute to a constant improvement of both the software and the implemented methods for the benefit of all users.

For further information please contact

This image shows Miriam Schulte

Miriam Schulte

Prof. Dr. rer. nat. habil.

Principal Investigator, Research Project D02

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