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μφ (muPhi)

Simulation of Flow and Transport in Porous Media

Scientific area

Modelling and simulation of water flow and solute transport in porous media, algebraic multi-grid solver.

Short description

Simulation of subsurface water flow and solute transport are crucial for the prediction and control of groundwater production, the assessment of water contamination and becomes more and more important for flood and climate prediction.

The highly scalable simulation program μφ for the solution of Richards' equation is capable to describe saturated and unsaturated subsurface flow. A cell-centred Finite-Volume scheme is used for the spatial discretisation, an implicit Euler scheme for the time discretisation and an incomplete Newton-scheme for the linearisation of the non-linear equations. The linear equation system is solved with the iterative solver template library (ISTL) developed by our group in the framework of the DUNE-Project. A BiCGstab solver with an algebraic multigrid preconditioner allows the efficient and scalable solution of huge systems on massively parallel computers.

In the transient solute transport part of μφ the Convection-Dispersion-Equation is solved on the flux fields generated by the water transport part using an explicit second-order Godunow discretisation with a minmod slope-limiter.

Both programs require massive data I/O (for the input parameter fields and the storage of solutions and flux fields. The usage of SIONlib allows for very efficient output on parallel file systems.

Matrix potential [Pa] (upper), volumetric water content [-] (middle) and permeability [m2] with 64 processes (8 x 8) and 512 x 512 x 128 grid cells.Matrix potential [Pa] (upper), volumetric water content [-] (middle) and permeability [m2] with 64 processes (8 x 8) and 512 x 512 x 128 grid cells.


  • 262,144 cores on BlueGene/P (JUGENE)
  • 458,752 cores (917,504 parallel processes) on BlueGene/Q (JUQUEEN)

Weak scaling of the water transport part and the solute transport part on JUQUEEN.Weak scaling of the water transport part and the solute transport part on JUQUEEN.

Programming language and model

Tested on platforms

  • BlueGene/Q and /P
  • x86

Application developers

  • Olaf Ippisch
  • Markus Blatt
  • Jorrit Fahlke
  • Felix Heimann


Olaf Ippisch
Universität Heidelberg
Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
Im Neuenheimer Feld 368
69120 Heidelberg

(Text and images provided by the developers)









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