Boundary conditions are a required component of the mathematical model to reduce boundary effects. They direct the motion of the flow and determine the behavior of the flowing fluid when it finds an obstacle, such as the geometry (structure) or the boundary of the domain. Numerically, the chosen boundary conditions dictate the values taken by the parameters to make it possible for the solvers to solve the flow differential equations. Different boundary conditions can be used in the flow direction and in the directions transverse to the flow.
One or more Computation Directions to apply the boundary conditions may be selected.
Select the directions where flow should be simulated. To obtain the flow results for all three directions in the result file, it is necessary to choose all three directions. To some extent, checking all directions for the run of the solver prolongs computational time.
Solving linear flow with Darcy Flow results in a 3x3 permeability matrix, which is only filled completely, if all computation directions are selected.
For Darcy Flow, the Boundary Conditions in Longitudinal Direction can be checked to be Periodic or Symmetric (Dirichlet). As Darcy Flow is used for structures with unresolved pores and low permeabilities, no inflow or outflow region should be given. Use symmetric boundary conditions for non-periodic structures if the percentage of solid voxels is high at the inlet. Otherwise, use periodic boundary conditions, as the simulation runtime is much faster.
In Darcy Flow simulations, the average Pressure at the Inlet surface and the average Pressure at the Outlet surface can be defined, where the pressure at outlet must be smaller than the pressure at inlet, since the pressure decreases from inlet to outlet. Select the desired pressure unit from the pull-down menu.
The Boundary Conditions in Transverse Directions can be checked to be Periodic, Symmetric, No-Slip, or Expert.
With the default Periodic selected, the process of periodic continuation is internally done during the run of the solver, repeatedly adding the volume structure in the directions transverse to the flow direction. Choosing the appropriate boundary condition depends on the structure’s design.
For example, imagine a structure with a cross-section as shown in (a).
If the expected pattern of the geometry is repeated in both transverse directions (b), the flow is computed with periodic boundary conditions.
If instead the geometry has mirror symmetry (c), symmetric boundary conditions are taken.
If the structure is encased in a closed wall (d), the no-slip boundary conditions are used in transverse directions.
The boundary conditions in the two directions transverse to the flow can also be set to be different by checking Expert boundary conditions. For example, when the fluid is chosen to flow in the Z-direction, the boundary conditions could be chosen to be No-slip in X-direction and Symmetric in the Y-direction. For Darcy Flow additionally to Periodic, Symmetric and No-Slip also No-Slip (fixed domain size) is available.
When No-Slip is used, the solver internally adds a one-voxel layer in the required direction and solves with periodic boundary conditions. That effectively is equivalent to solve the structure with casing in two ends in the direction of interest. So, the size of computation in this direction becomes n+1. However, if changing the computational size is not preferable, using No-Slip (fixed domain size) can avoid that, then the first layer of the structure is replaced by an impermeable material. Using the EJ solver runtimes are usually faster with No-Slip (fixed domain size) than with only No-Slip.
