The prediction of a conserved scalar is important in many fields of study. For example, in modeling of combustion processes, if a conserved scalar exists, the mathematical problem can be greatly simplified. Inert gases transported in mixtures of other gases are also simulated by a conserved scalar. This concept is also applicable to atmospheric sciences where pollutant dispersion can be studied by using a passive scalar approach.
Similarly, in oceanography, contaminant and nutrient transport can be studied using a passive scalar approach. Despite the substantial importance of conserved scalars, the predictive capability for their behavior in turbulent flows is hampered by the fact that the most popular methods for turbulent flow simulations are either not accurate, or not grid-spacing and discretization-order independent, or both. For example, the Reynolds Average Navier Stokes (RANS) method can be made grid-spacing independent by successively refining the grid until the results from the refinements coincide, but because of its inherent construct, RANS can only predict averages rather than detailed behavior. At the other extreme is the conventional Large Eddy Simulation (LES) in which the scales larger than a filter width are resolved and those smaller than the filter width are modeled using subgrid scale (SGS) models. These SGS models compute the contribution of the small scales using the solution at the larger scales that itself depends on the grid spacing. When the LES grid is refined, the SGS model changes, and thus a typical grid refinement study is not applicable. Therefore, simulations of turbulent transport of pollutants and nutrients in oceans are not predictive.
To remedy this situation, this work focused on re-formulating the model for such simulations so that it is predictive. The conventional LES equations were modified by using an additional explicit filter for the nonlinear terms. This additional filter removes the spurious small scales formed by aliasing.
The simulations for the conserved scalar are predictive in that they are independent of the grid-spacing on which the equations are solved, or on the discretization order used in the numerical method.