Sensitivity and uncertainty quantification techniques applied to systems of conservation laws

AbstractUncertainty quantification techniques are increasingly important in the interpretation of data and numerical simulations. Such techniques are typically employed either on data with poorly characterized underlying dynamics or on values from highly idealized model evaluations. We examine the application of these techniques to an intermediate case, in which data are generated from coupled, nonlinear partial differential equations—conservation laws—that admit discontinuous solutions. The values we analyze are generated from the numerical solution of the PDEs, in which we systematically vary both (i) fundamental modeling parameters and (ii) the underlying numerical algorithms. A number of sensitivity tests will be performed in order to assess the relative importance of such different types of uncertainty and we draw preliminary conclusions and speculate on the implications for more complex simulations