Janez Perko, Ravi A. Patel

Belgian Nuclear research Centre SCK•CEN, Institute for Environment Health and Safety, Mol, Belgium
Magnel Laboratory for Concrete Research , Department of structural engineering , Ghent University, Ghent, Belgium



Lattice-Boltzmann (LB) methods became widely used in many fields of science and engineering due to their computational efficiency and ability to deal with physical problems such as two phase flows which are less convenient to solve with traditional methods. Due to its simplicity most widely used approach for modeling advective diffusion equation is by LB-BGK formulation. However, LB-BGK formulations is less flexible in terms of time discretization and time step is limited by the choice of relaxation time in stability region defined by a physical diffusion coefficient and space discretization. This property poses even larger limitations when the diffusion coefficient is not constant throughout the computational domain. Typically in LB-BGK the variation in diffusion coefficient is accommodated through relaxation time during the collision step. This method is effective, but cannot deal with large diffusion coefficient variations which could be several orders of magnitude in real systems.
The method proposed in this paper explores alternative way of dealing with large diffusion coefficient variations in advective-diffusive transport systems by using so-called diffusion velocity which replaces variability in diffusion coefficients by additional advective term. In this way, the time step is defined by the reference diffusion coefficients and the variations from the reference diffusion by the advective fluxes which compensate for the remaining diffusion fluxes through the lattice.
In this paper the idea behind diffusion velocity formulation and its implementation into LB framework is presented. Further the benefits and limitations of the method are demonstrated on several advective-diffusive 1D and 2D examples.