Dimension-adaptive sparse grid for industrial applications using Sobol variances

The area of interest for this study is the field of uncertainty quantification in computational fluid dynamics. The goal is to contribute to a new method to perform uncertainty quantification analyses for industrial, computationally expensive CFD simulations. To this end, an adaptive grid refinement method is developed. The existing sparse grid procedure introduced by Smolyak is combined with Clenshaw-Curtis quadrature rules. Starting with a low level grid, more points are added based on the values of the Sobol variances, which are estimated values. The Sobol variances provide an indication of the importance of each variable and interactions between variables. The method is applied to an industrial atmospheric flow case, where a heavy gas is released upstream of a barrier. The quantity of interest is the effect distance, the distance from the barrier where the molar concentration drops below 1 percent, which is important for safety. The results show that, for this case, the new adaptive grid refinement method reduces the computational cost to one third of a conventional sparse grid, while providing similar results.