Permeability Convergence Study on 2D Pipes

Validation: FlowDict

The implementation of the Stokes equations in the LIR solver in FlowDict was validated on a 2D pipe by comparing the numerical results against the analytical solution.

The analytical solution can be calculated from the simple expression d2/32, with the channel width d = 20µm . The permeability computed with the flow solver depends strongly on the discretization of the no-slip boundary conditions. The no-slip boundary condition is discretized as described by Harlow-Welch (1965)1. A convergence study with increasing voxel resolution (from 2 to 64 voxel) shows that the numerical solution approaches the analytical permeability. Deviations below 2% are achieved with approximately 10 voxels.

References

1 Harlow, F.H. and Welch, J.E. “Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface” The Physics of Fluids, Volume 8, 1965

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