Stochastic Approaches to Quantify Solution Sensitivity to the Grid

Quantifying grid convergence is an essential component of predictive and reliable computational simulation. For many problems of practical interest involving tens of millions to hundreds of millions of degrees of freedom, this process is often impractical. Furthermore, techniques like implicitly-filtered Large Eddy Simulation lack a clear definition of grid convergence and only reach grid independence in a limit that is impossible to reach for relevant Reynolds numbers. In this work, an alternative process to assess the sensitivity of the solution to the grid is developed by treating the grid as a stochastic mesh. Rules based on allowable metrics, such as maximum stretching ratios, maximum skewness, etc., create correlations between the grid points, creating a system of dependent random variables. Novel non-intrusive, intrusive, and hybrid techniques to solve for the solution statistics using a stochastic mesh will be evaluated on representative problems. The result is a technique that can be used to guide improvements to the grid or that can serve as an alternative to quantifying grid convergence.