Optimum configuration for accurate simulations of chaotic porous media with Lattice Boltzmann Methods considering boundary conditions, lattice spacing and domain size

Abstract

Simulations of the flow field through chaotic porous media are powerful numerical challenges of special interest in science and technology. The simulations are usually done over representative samples which summarise the properties of the material. Several factors affect the accuracy of the results. Firstly the spatial resolution has to be fine enough to be able to capture the smallest geometrical details. Secondly the domain size has to be large enough to contain the large characteristic scale of the porous media. And finally the effects induced by the boundary conditions have to be diluted when more realistic options are not available. This is the case when the geometry is obtained by tomography and the periodic boundary conditions cannot be applied to delimit the sample because its geometry is not periodic. Impermeable boundary conditions are usually chosen to enclose the domain, forcing mass conservation. As a result, the flow field is over-restricted and the total pressure drop can be over-estimated. In this paper a new strategy is presented to optimise the computational resources consumption keeping the restrictions imposed by the accuracy criteria. The effects of the domain size, discretisation thickness and boundary condition disturbances are studied in detail. The study starts with the procedural generation of chaotic porous walls which mimics acicular mullite filters. An advantage of this process is the possibility to create periodic geometries. Periodicity permits the application of advanced techniques such as cyclic cross-correlations between the phase field and the velocity component fields without aliasing. From cross-correlation operations the large characteristic scale is obtained. The result is a lower threshold for the domain size. In second place a mesh independent study is done to find the upper threshold for the lattice spacing. The Minkowski–Bouligand fractal dimension of the fluid–solid interface corroborates the results. It has been demonstrated how the fractal dimension is a good candidate to replace the mesh independent study with lower computational cost for this type of problems. The last step is to compare the results obtained for a periodic geometry applying periodicity and symmetry as boundary conditions. Considering the periodic case as reference the resultant error is analysed. The explanation of the analysis includes how the intensity of the error changes in space and the limitations of symmetric boundary conditions.