Research Project A02

Advanced modelling concepts for coupling free flow with porous-media flow


Data sets published by project A02 can be found on the DaRUS website

Publications in scientific journals

  1. Conference papers

    1. Chu, X., Wang, W., Müller, J., Von Schöning, H., Liu, Y., & Weigand, B. (2021). Turbulence Modulation and Energy Transfer in Turbulent Channel Flow Coupled with One-Side Porous Media. In W. E. Nagel, D. H. Kröner, & M. M. Resch (Eds.), High Performance Computing in Science and Engineering ’20 (pp. 373--386). Springer International Publishing.
    2. Chu, X., Müller, J., & Weigand, B. (2021). Interface-Resolved Direct Numerical Simulation of Turbulent Flow over Porous Media. In W. E. Nagel, D. H. Kröner, & M. M. Resch (Eds.), High Performance Computing in Science and Engineering ’19 (pp. 343--354). Springer International Publishing.
    3. Müller, J., Offenhäuser, P., Reitzle, M., & Weigand, B. (2020). A Method to Reduce Load Imbalances in Simulations of Solidification Processes with Free Surface 3D. In M. M. Resch, Y. Kovalenko, W. Bez, E. Focht, & H. Kobayashi (Eds.), Sustained Simulation Performance 2018 and 2019 (pp. 163--184). Springer International Publishing.
    4. 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. Boon, W. M., Gläser, D., Helmig, R., Weishaupt, K., & Yotov, I. (2024). A mortar method for the coupled Stokes-Darcy problem using the MAC scheme for Stokes and mixed finite elements for Darcy. Computational Geosciences.
    2. Aricò, C., Helmig, R., Puleo, D., & Schneider, M. (2024). A new numerical mesoscopic scale one-domain approach solver for free fluid/porous medium interaction. Computer Methods in Applied Mechanics and Engineering, 419, 116655.
    3. Mohammadi, F., Eggenweiler, E., Flemisch, B., Oladyshkin, S., Rybak, I., Schneider, M., & Weishaupt, K. (2023). A surrogate-assisted uncertainty-aware Bayesian validation framework and its application to coupling free flow and porous-medium flow. Computational Geosciences.
    4. Boon, W. M., Gläser, D., Helmig, R., & Yotov, I. (2023). Flux-mortar mixed finite element methods with multipoint flux approximation. Computer Methods in Applied Mechanics and Engineering, 405, 115870.
    5. Wu, H., Veyskarami, M., Schneider, M., & Helmig, R. (2023). A New Fully Implicit Two-Phase Pore-Network Model by Utilizing Regularization Strategies. Transport in Porous Media.
    6. Ackermann, S., Fest-Santini, S., Veyskarami, M., Helmig, R., & Santini, M. (2023). Experimental validation of a coupling concept for drop formation and growth onto porous materials by high-resolution X-ray imaging technique. International Journal of Multiphase Flow, 160, 104371.
    7. Veyskarami, M., Michalkowski, C., Bringedal, C., & Helmig, R. (2023). Droplet Formation, Growth and Detachment at the Interface of a Coupled Free-FLow--Porous Medium System: A New Model Development and Comparison. Transport in Porous Media.
    8. Ahmadi, N., Muniruzzaman, M., Sprocati, R., Heck, K., Mosthaf, K., & Rolle, M. (2022). Coupling soil/atmosphere interactions and geochemical processes: A multiphase and multicomponent reactive transport approach. Advances in Water Resources, 104303.
    9. Wang, W., Lozano-Durán, A., Helmig, R., & Chu, X. (2022). Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media. Journal of Fluid Mechanics, 949, A16--. 10.1017/jfm.2022.770
    10. Ahmadi, N., Heck, K., Rolle, M., Helmig, R., & Mosthaf, K. (2021). On multicomponent gas diffusion and coupling concepts for porous media and free flow: a benchmark study. Computational Geosciences.
    11. Haide, R., Fest-Santini, S., & Santini, M. (2021). Use of X-ray micro-computed tomography for the investigation of drying processes in porous media: A review. Drying Technology, 1--14.
    12. Weishaupt, K., & Helmig, R. (2021). A dynamic and fully implicit non-isothermal, two-phase, two-component pore-network model coupled to single-phase free flow for the pore-scale description of evaporation processes. Water Resources Research.
    13. Wang, W. (王文康), Yang, G. (杨光), Evrim, C., Terzis, A., Helmig, R., & Chu, X. (初旭). (2021). An assessment of turbulence transportation near regular and random permeable interfaces. Physics of Fluids, 33(11), Article 11.
    14. Koch, T., Weishaupt, K., Müller, J., Weigand, B., & Helmig, R. (2021). A (Dual) Network Model for Heat Transfer in Porous Media. Transport in Porous Media.
    15. Schneider, M., Weishaupt, K., Gläser, D., Boon, W. M., & Helmig, R. (2020). Coupling staggered-grid and MPFA finite volume methods for free flow/porous-medium flow problems. Journal of Computational Physics, 401.
    16. Schout, G., Hartog, N., Hassanizadeh, S. M., Helmig, R., & Griffioen, J. (2020). Impact of groundwater flow on methane gas migration and retention in unconsolidated aquifers. Journal of Contaminant Hydrology, 230, 103619.
    17. Weishaupt, K., Terzis, A., Zarikos, I., Yang, G., Flemisch, B., de Winter, D. A. M., & Helmig, R. (2020). A Hybrid-Dimensional Coupled Pore-Network/Free-Flow Model Including Pore-Scale Slip and Its Application to a Micromodel Experiment. Transport in Porous Media.
    18. Bahlmann, L. M., Smits, K., Heck, K., Coltman, E., Helmig, R., & Neuweiler, I. (2020). Gas Component Transport across the Soil-Atmosphere-Interface for Gases of Different Density: Experiments and Modeling. Water Resources Research.
    19. Koch, T., Gläser, D., Weishaupt, K., Ackermann, S., Beck, M., Becker, B., Burbulla, S., Class, H., Coltman, E., Emmert, S., Fetzer, T., Grüninger, C., Heck, K., Hommel, J., Kurz, T., Lipp, M., Mohammadi, F., Scherrer, S., Schneider, M., … Flemisch, B. (2020). DuMux 3 – an open-source simulator for solving flow and transport problems in porous media with a focus on model coupling. Computers & Mathematics with Applications.
    20. Heck, K., Coltman, E., Schneider, J., & Helmig, R. (2020). Influence of Radiation on Evaporation Rates: A Numerical Analysis. Water Resources Research, 56(10), Article 10.
    21. de Winter, D. A. M., Weishaupt, K., Scheller, S., Frey, S., Raoof, A., Hassanizadeh, S. M., & Helmig, R. (2020). The Complexity of Porous Media Flow Characterized in a Microfluidic Model Based on Confocal Laser Scanning Microscopy and Micro-PIV. Transport in Porous Media.
    22. Chu, X., Wang, W., Yang, G., Terzis, A., Helmig, R., & Weigand, B. (2020). Transport of Turbulence Across Permeable Interface in a Turbulent Channel Flow: Interface-Resolved Direct Numerical Simulation. Transport in Porous Media.
    23. Chu, X., Wu, Y., Rist, U., & Weigand, B. (2020). Instability and transition in an elementary porous medium. Phys. Rev. Fluids, 5(4), Article 4.
    24. Yang, G., Vaikuntanathan, V., Terzis, A., Cheng, X., Weigand, B., & Helmig, R. (2019). Impact of a Linear Array of Hydrophilic and Superhydrophobic Spheres on a Deep Water Pool. Colloids Interfaces, 3(1), Article 1.
    25. Chu, X., Yang, G., Pandey, S., & Weigand, B. (2019). Direct numerical simulation of convective heat transfer in porous media. International Journal of Heat and Mass Transfer, 133, 11--20.
    26. Weishaupt, K., Joekar-Niasar, V., & Helmig, R. (2019). An efficient coupling of free flow and porous media flow using the pore-network modeling approach. Journal of Computational Physics: X, 1.
    27. Terzis, A., Zarikos, I., Weishaupt, K., Yang, G., Chu, X., Helmig, R., & Weigand, B. (2019). Microscopic velocity field measurements inside a regular porous medium adjacent to a low Reynolds number channel flow. Physics of Fluids, 31(4), Article 4.
    28. Yang, G., Terzis, A., Zarikos, I., Hassanizadeh, S. M., Weigand, B., & Helmig, R. (2019). Internal flow patterns of a droplet pinned to the hydrophobic surfaces of a confined microchannel using micro-PIV and VOF simulations. Chemical Engineering Journal, 370, 444--454.
    29. Sauer, E., Terzis, A., Theiss, M., Weigand, B., & Gross, J. (2018). Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State. Langmuir, 34(42), Article 42.
    30. Chu, X., Weigand, B., & Vaikuntanathan, V. (2018). Flow turbulence topology in regular porous media: From macroscopic to microscopic scale with direct numerical simulation. Physics of Fluids, 30(6), Article 6.
    31. Yang, G., Weigand, B., Terzis, A., Weishaupt, K., & Helmig, R. (2018). Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures. Transport in Porous Media, 122(1), Article 1.


About this Project

Exchange processes across a porous-medium free-flow interface occur in a wide range of environmental, technical and bio-mechanical systems. The primary objectives of this project are to (i) analyse and improve the theory, as well as (ii) offer solution methods for non-isothermal, multi-phase, multi-component flow and transport processes at a porous-medium free-flow interface and (iii) investigate the influence of these processes on both the porous medium and free-flow region for various application scales.

Exchange processes at the free-flow porous-medium interface at different scales


The challenge of including scale-dependent, interface-driven processes into mathematical and numerical models for systems of coupled free flow and porous-medium flow is the primary object of research of project A02. We found that existing models usually operate on either the pore scale or on the REV scale which has the following drawbacks: pore-scale models provide a detailed physical insight into various types of processes but their prohibitively high computational demand makes them only applicable to relatively small domains. On the other hand, the higher degree of computational efficiency provided by REV-scale models comes at the price of losing potentially process-relevant sub-scale information. In addition, several assumptions and simplifications commonly involved in REV-scale modelling can only be justified for a limited range of applications and flow conditions.

Our main goal is the development of new model concepts combining the strengths of both pore-scale and REV-scale approaches.

One focus point is the numerical investigation of interface exchange processes on the pore scale for highly resolved porous geometries and how characteristics of the pore geometry contribute to macro-scale quantities. This can then be integrated into the second focus point, the incorporation of pore-scale effects into REV-scale modelling approaches. This aims to improve the sometimes oversimplified interface conditions on REV-scale models. One of the key goals is the development of an interface-region approach where a pore-network model is used to couple a free-flow domain and a bulk porous region.

We developed interface conditions for the coupling between the free-flow domain and the pore-network model, ensuring the conservation mass and momentum across the discrete pore-scale coupling interface. Following this, conditions for coupling the pore-network model with the REV-scale bulk porous medium were developed, resulting in a three-domain model concept where the pore-network models serves as an interface region between the free-flow domain and the bulk porous part. The coupled free-flow/pore network model was extended for non-isothermal, multi-component two-phase flow in the network part, allowing the simulation of an evaporation process in ample detail. For the regular porous domain under consideration, we identified a dominating influence of advective mass transport during stage-II evaporation, which is usually governed by diffusion. The validation of the hybrid-dimensional model for two-phase flow with experimental data is part of ongoing work. First promising results of microPIV investigations on partly saturated micromodels have been obtained by our collaboration partner at Utrecht University.

Another focus point of project A02 is the extension of the analysis of coupled porous-medium free-flow processes to more complex scenarios and processes. For this purpose we investigated turbulent free flow over non-planar surfaces and its effect on evaporation, as well as the influence of solar radiation. Supported by wind-tunnel experiments, we investigated the interfacial exchange processes for gases of different density to extend the analysis of multi-component transport.

Future Work

Extension of the hybrid approach and development of new multi-scale model concepts that allow to accurately describe interface processes. A special focus is to analyse the influence of surface roughness, surface topology and soil heterogeneities on mass, momentum and energy transfer across the interface for single-phase and multi-phase systems. Such analyses can be systematically performed on different scales using appropriate numerical models, i.e. pore-scale and macro-scale models, and validated with experimental data.

International Cooperation

Utrecht University

Our collaboration partners at Utrecht University provide us with pore-scale experimental data based on micro-particle image velocimetry (µPIV) for the development and validation of our numerical models. Profiting from a fully-equipped lab and years of experience with microfluidic experuments, we study free flow adjacent to porous media using micro models made of Polydimethylsiloxane (PDMS) and confocal laser scanning microscopy.

In cooperation with our partner, we first considered single-phase free flow above an array of regular square obstacles. In a next step, the data acquisition and evaluation procedure was further developed and automated to a large extend and we were able to reconstruct  three-dimensional flow fields.

Regarding two phases, the physics of a droplet of immiscible liquid pinned to a solid wall adjacent to free-flow was investigated in a µPIV experiment and recalculated successfully using the volume of fluids method (VOF).

We are currently working on a micromodel experiment with single-phase free flow above a porous domain featuring two phases.Using tracer particles in both fluid phases,the interphasial momentum transfer can be assessed which is essential for the extension of the widely-used Beavers-Joseph condition for modelling two-phase flow on the REV scale.

University of Pittsburgh / KTH Royal Institute of Technology

We developed a novel mortar coupling approach  which guarantees flux conservation in cooperation with our international partners (More information can be found under the internal project I-01). We envisage to extend and further develop these concepts.


University of Bergamo

The external partners provide expert knowledge for the detailed measurement of complex pore structures and XRCT which allow the accurate three-dimensional mapping of solid bodies. Pore-network models (PNM) can be extracted from XRCT volume data sets.

For further information please contact

This image shows Rainer Helmig

Rainer Helmig

Prof. Dr.-Ing. Dr.-Ing. h.c.

Principal Investigator, Former Spokesperson, Research Projects A02 and C02, Central Project Z

This image shows Bernhard Weigand

Bernhard Weigand

Prof. Dr.-Ing. habil.

Principal Investigator, Research Project A02

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