A lattice-Boltzmann (LB) formulation is developed for the simulation of Cattaneo’s diffusion equation. To do this, the collision term is computed from a 1-step back relaxation dynamics which, in turn, induces a hyperbolic-type diffusion effect. The Fickian LB formulation is recovered in the...

This paper studies reaction–diffusion phenomena in disordered porous media with non-Fickian diffusion effects. The aim is to obtain an effective medium equation of the concentration dynamics having a fractional Fick's law description for the particles flux. Since the methodology is based on a...

Up-scaling of the Stokes equations with non-slip boundary condition describing the flow in a porous medium, leads to the Darcy–Brinkman equationɛβμβvD,β=-Kβ·(∇Pm,β-ρβg)+Kβ·μβ∇2vD,β.The second-order term -μβ∇2vD,β recovers the viscous drag effects and uses the fluid...

This paper focuses on the reaction-diffusion problem in a disordered porous medium. The objective is to obtain an effective medium description of the concentration dynamics having a fractional Cattaneo's law equation as the flux constitutive equation. The methodology is based on a volume...

In this paper, a high-order generalization of the diffusion Cattaneo's equation is considered. A class of admissible linear relaxation dynamics is characterized by computing the impedance of a simple diffusion process. Some examples are used to illustrate the results.