Generation of a One-Parameter Family of Residuals for the Filtered Equations of Fluid Motion

Analysis based on Galilean invariance [1] and more recently of positive definiteness [2] are useful in approaching some kind of validation for proposed subgrid scale models used in large eddy simulations. In [3] an attempt is made to construct general formulae for the residual stress-strain in terms of the macroscale variables (equivalently the filtered fields) based on a model error. In [4] it was demonstrated how much formulae could form a template for the discretization scheme and how the differencing coefficients and emperical parameters of the model can be associated. It was suggestive of exploiting the degrees of freedom of the coupled system of emperical and numerical diffrence coefficients to investigate the possible employment of constraints which capture the dominant dissipative-dispersive characteristics of the application. The process also demonstrates how the subgrid scale model can be isolated from the discretization error.