Solver technology

in GeoDict

Various solvers, each suitable for different process parameters and material properties, are available to solve equations under the prediction modules of GeoDict (e.g., in FlowDict).

By operating directly on voxel geometries, our solvers eliminate the need for manual meshing required in other simulation software. The low memory requirements of our solvers are optimal for simulations on large voxel geometries. Some solvers may be used to solve various physical equations.


EJ Solver (Explicit Jump)

The EJ solver (Explicit Jump) can be used to solve the Stokes and Darcy equations (e.g., in FlowDict) and conduction equations (e.g., in ConductoDict or DiffuDict). The solver uses a uniform grid to discretize the unknown variables (e.g., velocity and pressure). The Stokes and conductivity equations are solved using Fast Fourier Transformation and the introduction of jump variables at the no-slip boundary conditions, as well as material interfaces.

The solver is very efficient in solving the Stokes equations for highly porous media (over 90% porosity). Moreover, it is exceptionally well-suited to solve conductivity equations in porous media with significant differences in conductivity.


SimpleFFT Solver

The SimpleFFT solver can be used to solve the (Navier-)Stokes(-Brinkman) equations and also utilizes a uniform grid to discretize velocity and pressure. This solver employs the SIMPLE (Semi-implicit Method for Pressure Linked Equations) method to solve the (Navier-)Stokes(-Brinkman) equations. In this approach, the momentum balance and pressure correction equations are solved alternately. What sets this solver apart is that the pressure correction equation is solved using Fast Fourier Transformation.

The solver is excellent for low-porous geometries (e.g. below 50% porosity), such as digital rocks.


LIR Solver

The LIR solver supports various physical equations and can be used for flow, conductivity, battery, and mechanics simulations. In contrast to other solvers, this solver employs an adaptive grid instead of a uniform grid to discretize sought quantities, such as velocity and pressure. The technology behind this adaptive grid is referred to as the LIR tree, which is a combination of Octree and KD-tree.

In flow simulations, the pore space in the center of large pores is coarsened, where velocity and pressure vary only slightly. Near solid surfaces, the original voxel resolution is maintained. The momentum balance and mass conservation equations are solved simultaneously in the solution process, with various acceleration options available (e.g., Multigrid and Krylov subspace methods).

The solver is very fast for both high and low porosity media and requires minimal memory usage.