Grid resolution

Figure 4-13 shows an example from a three-dimensional model simulation of the global atmospheric sulfur balance (Feichter et al, 1996). The model had a grid resolution of about 500 km in the horizontal and on average 1 km in the vertical. The chemical scheme of the model included emissions of dimethyl sulfide (DMS) from the oceans and SO2 from industrial processes and volcanoes. Atmospheric DMS is oxidized by the hydroxyl radical to form SO2, which, in turn, is further oxidized to sulfuric acid and sulfates by reaction with either hydroxyl radical in the gas phase or with hydrogen peroxide or ozone in cloud droplets. Both SO2 and aerosol sulfate are removed from the atmosphere by dry and wet deposition processes. The reasonable agreement between the simulated and observed wet deposition of sulfate indicates that the most important processes affecting the atmospheric sulfur balance have been adequately treated in the model. 

It is readily apparent that finer and finer structures get resolved as the number of spatial grids is increased. Statistical quantities, such as average slip velocity between the gas and particle phases, obtained by averaging over the whole domain, were found to depend on the grid resolution employed in the simulations and they became nearly grid-size independent only when grid sizes of the order of a few ( 10) particle diameters were used. Thus, if one sets out to solve microscopic TFM equations, grid sizes of the order of few particle... 

A final piece of the proof-of-concept calculations is to compare the predictions obtained by solving the filtered TFM equations with highly resolved simulations of the microscopic TFM equations. For this purpose, Andrews and Sundaresan (2005) performed simulations of the microscopic TFM equations in a 16 x 32 cm periodic domain at various resolutions (e.g., see Fig. 29). From these simulations, they extracted domain-average quantities in the statistical steady state (see Agrawal et al., 2001 for a discussion of how these data are gathered). Fig. 33 shows the domain-average slip velocity between the gas and particle phases at various grid resolutions (shown by the squares connected by... 

Another result that is not evident in Fig. 33 concerns the computational times required for gathering the statistical steady-state values of various quantities (such as the slip velocity shown in Fig. 33) at comparable grid resolutions, the computational time required to solve the filtered equations is much smaller than that for the microscopic equations. This can be attributed to the fact that the structures obtained in the solution of the filtered equations are comparatively coarser than those for the microscopic TFM equations. 

Dore AJ, Kryza M, Hall JR, Hallsworth S, Keller VJD, Vieno M, Sutton MA (2012) The influence of model grid resolution on estimation of national scale nitrogen deposition and exceedance of critical loads. Biogeosciences 9 1597-1609... 

Figure 5 Effect of grid resolution (A.) on the time-averaged dimensionless slip velocity (us/uT). Geldart group A particles are used. The ordinate is scaled with the terminal velocity of single particles (uT 21.84 cm/s) and the abscissa is scaled with the particle diameter dp. The domain size is 1.5 x 6 cm2, comparable to the coarse-grid used in normal simulations.

Figure 8 compares Model M with Model G in terms of their predictions of the axial profiles of voidage under various grid resolutions. For FCC particles, when using Model G, the solids were distributed uniformly across the riser height. It seems that the grid refining has little... 

Figure 8 Axial profiles of cross-sectionally averaged voidage under different grid resolutions for IPE and ETH risers.

The two sets of conservative equations defined by Eq. (8.2) and Eqs. (8.2)-(8.2) describe turbulent reacting two-phase flows that require a high grid resolution in order to solve from the smallest to the largest scales. In LES only the largest scales are computed while the smallest scales are modeled. 

The authors concluded that field conditions could be reproduced by both wind tunnel and numerical models, but the numerical models were very sensitive to alternative specifications of grid resolution, wall boundary conditions, source size and turbulence... 

Fortunately, numerical modeling despite its many limitations associated with grid resolution, choice of turbulence model, or assignment of boundary conditions is not intrinsically limited by similitude or scale constraints. Thus, in principle, it should be possible to numerically simulate all aspects of fires within canopies for which realistic models exist for combustion, radiation, fluid properties, ignition sources, pyrolysis, etc. In addition it should be possible to examine all interactions of fire properties individually, sequentially and combined to evaluate nonlinear effects. Thus, computational fluid dynamics may well provide a greater understanding of the behavior of small, medium, and mass fires in the future. 

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