Sensitivity analysis techniques applied to a system of hyperbolic conservation laws

Sensitivity analysis is comprised of techniques to quantify the effects of the input variables on a set of outputs. In particular, sensitivity indices can be used to infer which input parameters most significantly affect the results of a computational model. With continually increasing computing power, sensitivity analysis has become an important technique by which to understand the behavior of large-scale computer simulations. Many sensitivity analysis methods rely on sampling from distributions of the inputs. Such sampling-based methods can be computationally expensive, requiring many evaluations of the simulation; in this case, the Sobol' method provides an easy and accurate way to compute variance-based measures, provided a sufficient number of model evaluations are available. As an alternative, meta-modeling approaches have been devised to approximate the response surface and estimate various measures of sensitivity. In this work, we consider a variety of sensitivity analysis methods, including different sampling strategies, different meta-models, and different ways of evaluating variance-based sensitivity indices. The problem we consider is the 1-D Riemann problem. By a careful choice of inputs, discontinuous solutions are obtained, leading to discontinuous response surfaces; such surfaces can be particularly problematic for meta-modeling approaches. The goal of this study is to compare the estimated sensitivity indices with exact values and to evaluate the convergence of these estimates with increasing samples sizes and under an increasing number of meta-model evaluations.