A posteriori analysis of numerical errors in subfilter scalar variance modeling for large eddy simulation

Abstract

Subfilter scalar variance is a critical indicator of small scale mixing in large eddy simulation (LES) of turbulent combustion and is an important parameter of conserved scalar based combustion models. Realistic combustion models have a highly nonlinear dependence on the conserved scalar, making the prediction of flow thermochemistry sensitive to errors in subfilter variance modeling, including errors due to numerical discretization. Large numerical errors can result from the use of grid-based filtering and the resulting under-resolution of the smallest filtered scales, which are a key to variance modeling. Hence, the development of variance models should take into account this sensitivity to numerical discretization. In this work, a novel coupled direct numerical simulation (DNS)-LES a posteriori method is used to study the role of discretization errors in variance prediction for the two most widely used types of models: algebraic dynamic models and transport equation-based models. Algebraic models are found to be ill-suited to discretization due to their dependence on filtered scalar gradient values. Additionally, the use of dynamic modeling procedures enhances their sensitivity to filtered scalar errors. The accuracy of transport equation models primarily rests on the accuracy of the scalar dissipation rate closure with numerical error having a secondary effect. The influence of dissipation rate modeling error is investigated using the unique information provided by the combined DNS-LES simulation method. Overall, transport equation models are found to offer a more powerful approach to variance modeling due to more complete model physics and reduced effects of discretization error.