Subfilter Mixture Fraction Variance Model Parameter Sensitivity

Abstract

The sensitivity of the mixture fraction variance in a bluff body flow is analyzed. Two partial differential equation (PDE) methods, the forward and adjoint methods, are employed to compute the sensitivity with respect to two model parameters: a dissipation coefficient in the mixture fraction variance PDE and the Schmidt number, which here is used as a subfilter diffusivity model coefficient. The relative magnitudes of these sensitivities are discussed. Bootstrapping is presented as a means for stabilizing an adjoint PDE. In addition to the two PDE implementations, algebraic approximations of these sensitivities are derived. The accuracy of the PDE methods and algebraic approximations are computationally validated.