Simulations of heat transport in porous mediums are a challenge for computational study due to the multiple length and time scales.  The coupled porous structure generation and heat transport simulation methods in mesoscale is introduced. Both numerical schemes are based on probability distribution functions in Gaussian quadrature grid and velocity sets.  The mesoscale method for various structure generations, which named as the controllable structure generation scheme, can be applied to generate not only multiple-phase isotropic homogenous random structures, but also shape-constrained anisotropic heterogeneous structures through relatively simple constraint integer indexes with a high accuracy of global phase volume fractions no larger than the ratio of one grid volume size over the whole volume.  The non-dimensional lattice Boltzmann method for coupled transport equations for heat transfer and fluid flow can be applied for direct mesoscale simulations of thermal diffusion and natural convection in the generated structures described by the local phase volume fraction matrix. The variable time-step scheme with adjustable mesoscopic March numbers and the stretched mesh scheme with varying local coordinate transformation gradients are compared those fixed time and mesh methods. The effective parallel schemes with minimum information transferred during the data communication between subdomains will be illustrated. Various results of thermal diffusion and natural convection through porous mediums including sphere, fiber, foam, and random porous pellet packed structures are presented to provide a better understanding of the underlying mechanism of heat transport in porous media.

Reference: Y. Su, “Mesoscopic scale simulations of heat transport in porous structures”, Advances in Heat Transfer Vol. 55, Chapter 4, Elsevier, 2023.