Advanced Flow Simulations with enhanced Accuracy

GeoDict features the solvers EJ, LIR, and Simple-FFT for simulating fluid flow in porous media. The accuracy of these simulations is significantly influenced by voxel resolution and the underlying numerical discretization techniques. This is especially important for high-speed flows in complete filters and flows through narrow channels in filter cakes, or dense rocks such as shales or carbonates. GeoDict 2025 introduces a suite of new features aimed at enhancing simulation accuracy and aligning simulations more closely with experimental measurements. In this presentation, we will showcase these new capabilities and illustrate their effectiveness in various applications.

The LIR solver can utilize an adaptive grid. Previously, only allowing cells to be larger than a single voxel, thereby enhancing performance by reducing runtime and memory usage. A major enhancement in GeoDict 2025's LIR solver is the support for computational cells smaller than the voxel length. Additionally, a new refinement criterion, known as the “a posteriori error bound”, has been implemented. These improvements enable grid refinement in areas requiring higher accuracy, even when the initial voxel grid lacks sufficient resolution which is often the case for digital rocks. The grid can now also be adapted based on local Reynolds numbers, which is particularly beneficial for fast Navier–Stokes flows where regions with strong vortices need precise resolution.

For even faster flows, turbulent behavior may arise, and a stationary flow field may not exist. In such cases, solving the transient Navier–Stokes equations become necessary. A first step towards this development is Direct Numerical Simulations (DNS), where vortices are directly resolved, and time steps are computed sequentially. We will present the results of the validation with the well-known Kármán vortex street. In future GeoDict versions, we will be able to use this capability for Large Eddy Simulations (LES).

Additionally, for EJ, Simple-FFT, and LIR, two new no-slip boundary condition discretizations are introduced: “Second Order” and “Sharp Corner”. The Second Order method sets the tangential velocity to zero at the center of the voxel surfaces using a second-order polynomial approximation, achieving more accurate results at the same resolution. The Sharp Corner method sets the tangential velocity to zero at voxel corners and is particularly effective for digital rock simulations, where permeability is often overestimated.