Bayesian Inversion and Regression Trees for Mixing Length Model Development

Current trends in computational fluid dynamics (CFD) sees numerical models developed primarily through parameter tuning, which is in turn based on experiments and intuition. Whilst such approaches have been traditionally useful, they are now becoming difficult to manage due to their sheer complexity, and specificity to particular flow problems. This in turn leads to CFD solutions with increased computational complexity, and little benefit in the overall accuracy or validity of the final solution. Moreover, these analytical methods do not make full use of existing direct numerical simulation (DNS) datasets. Therefore, in this paper an innovative method of improving a CFD wall model through the use of classic big-data techniques will be investigated. These techniques will make full use of current DNS by looking for important flow features, and fitting optimal regressors in order to validate and simplify current CFD wall models. This will be achieved by using a Bayesian methodology to correct a mixing length model, coupled with a regression tree to infer solutions at various friction Reynolds numbers.