Flow Simulation


The FlowDict module predicts effective material properties (flow velocity, flow permeability, and flow resistivity) by simulating flow experiments and post-processing the simulation results.

A flow experiment in FlowDict requires the input of a:

  • 3D representation of a structure or material 
  • Newtonian fluid (gas or liquid) with constant density (incompressible) 
  • Experimental process parameters, such as mass flow rate, pressure difference and flow direction.

Examples of Applications

  • Determine air and water permeability in woven fabrics 
  • Study gas and liquid permeability and pressure drop in filter media 
  • Predict the absolute permeability on digital rocks

Examples of Applications

FlowDict Features

FlowDict can perform three categories of calculations:

  • Prediction of mean flow velocity for a given pressure drop 
  • Prediction of the pressure drop for a given mean flow velocity 
  • Prediction of the full or partial permeability tensor

Post-Processing in FlowDict

In post-processing, FlowDict uses Darcy's law to compute the material permeability using mean flow velocity, fluid viscosity, pressure drop, and media thickness. Darcy's law only applies to very slow flows (Stokes flows) with a Reynolds number of zero.

Faster flows are described by the Navier-Stokes equation. For faster flows, the relationship between pressure drop and mean velocity is not linear.

For slow and faster flows, FlowDict assumes a steady flow regime, without time-dependent behavior such as turbulence. Thus, velocity and pressure drop cannot be arbitrarily high. 

FlowDict computes stationary fluid flows described by the equations:

  • Stokes (with EJ, SimpleFFT, or LIR solver) 
  • Stokes-Brinkman (with SimpleFFT or LIR solver)
  • Navier-Stokes (with SimpleFFT or LIR solver)
  • Navier-Stokes-Brinkman (with SimpleFFT or LIR solver)

For very fast flows, where no stationary solution exists, the pressure drop or mean velocity can be approximated with Forchheimer Approximation.

FlowDict also provides an export to perform flow simulations with third-party software: 

  • Navier-Stokes (Fluent) 

Solver technologies in FlowDict

FlowDict bundles three solver technologies, each suitable for different materials:

Explicit Jump (EJ)

uses a uniform grid to discretize velocity and pressure. The solver is very fast for highly porous materials (e.g. filter media).


also uses a uniform grid and is very fast for low porous materials (e.g. digital rocks).

LIR solver

uses an adaptive grid structure, is extremely fast for highly porous materials, and requires very little memory.

Darcy solver

In GeoDict2023 it is possible to directly solve the Darcy equation using the new Darcy flow simulation command in FlowDict! It is suited for flow simulations on large medical CT scans and is much faster and more memory efficient than the Stokes-Brinkman solvers.

Additional modules needed?

Modules Applications
GeoDict Base  Includes the basic functionality of GeoDict [necessary]
ImportGeo-Vol  Import and segmentation of the µCT images and generation of the 3D microstructure models based on them [optional]
Digitale Material Design  Application-relevant modules for creating and modeling 3D microstructure models in GeoDict [optional]

FlowDict is required for other modules to function

Modules Applications
FilterDict the solvers of FlowDict for computing flow fields as well as the pressure drops or mean velocities
AddiDict Stokes solver for computing flow fields
AcoustoDict Stokes solver for computing permeability
SatuDict Stokes solver for computing relative permeability