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Use of the effective diffusion coefficient and the artificial grid diffusion coefficients are found to be effective to stabilize the acceleration calculation in highly voided conditions.
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The methodology was designed to model all the particle diffusion in RANS regions and model only the sub-grid diffusion in LES regions.
The combination of resolved diffusion and sub-grid diffusion compared quite reasonably with diffusion based on Direct Numerical Simulation of the Navier Stokes equations.
At the next moment in time (t = 1), the dye molecules have the ability to access a larger area of our grid through diffusion.
In the governing PDE, a shock indicator acts as a forcing term while grid-based diffusion is added to smooth the resulting artificial viscosity.
The stabilisation mechanism of the flame was dominated by the convection and sub-grid scale diffusion of hot combustion products from the recirculation zone to the cold gases that enter the burner, as revealed by analysis of the CMC equation.
Useful comparisons can also be made with Craine et al. (2005) and Craine (2006), where continuous-time uptake and growth mechanisms are employed to model root growth and competition, using a spatially explicit set of 2D (horizontal and vertical) root growth simulations and grid-based diffusion at small (cm) scales.
From this relation, we chose diffusion grid size nc = 50 μm, and consequently, each diffusion grid contains 10 × 10 × 10 cells.
The use of a structured population - a spatial distribution of individuals in the form of either a set of islands or a diffusion grid - determines the dynamical processes that can take place in complex systems.
For instance, at each time-step within a diffusion grid, the total amount of nutrients consumed should be considerably smaller than available nutrients.
In order to account for both possibilities, the model was tested in two structured settings: a 2-dimensional grid with limited diffusion and a community network in which small groups of hosts closely interact with each other.
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