How to Calculate Tortuosity Easily?

Tortuosity is one of the key parameters describing the geometry and transport properties of porous media. It is defined either as an average elongation of fluid paths or as a retardation factor that measures the resistance of a porous medium to the flow. However, in contrast to a retardation factor, an average fluid path elongation is difficult to compute numerically and, in general, is not measurable directly in experiments. We review some recent achievements in bridging the gap between the two formulations of tortuosity and discuss possible method of numerical and an experimental measurements of the tortuosity directly from the fluid velocity field.Comment: 6 pages, 8 figure

Study of the convergence of the Meshless Lattice Boltzmann Method in Taylor-Green and annular channel flows

The Meshless Lattice Boltzmann Method (MLBM) is a numerical tool that relieves the standard Lattice Boltzmann Method (LBM) from regular lattices and, at the same time, decouples space and velocity discretizations. In this study, we investigate the numerical convergence of MLBM in two benchmark tests: the Taylor-Green vortex and annular (bent) channel flow. We compare our MLBM results to LBM and to the analytical solution of the Navier-Stokes equation. We investigate the method's convergence in terms of the discretization parameter, the interpolation order, and the LBM streaming distance refinement. We observe that MLBM outperforms LBM in terms of the error value for the same number of nodes discretizing the domain. We find that LBM errors at a given streaming distance $\delta x$ and timestep length $\delta t$ are the asymptotic lower bounds of MLBM errors with the same streaming distance and timestep length. Finally, we suggest an expression for the MLBM error that consists of the LBM error and other terms related to the semi-Lagrangian nature of the discussed method itself