Uncertainty propagation of the shock position for hyperbolic PDEs using a sensitivity equation method


In this work, we design a method to provide confidence intervals for the position of a discontinuity arising in hyperbolic conservation laws when some of the parameters of the problem are uncertain. This is based on a sensitivity equation method, therefore can be used only if the variance of the uncertain parameters is small. We illustrate how this method works on a simple one-dimensional conservation law: the inviscid Burgers equation. Multiple test cases are defined, some for which the analytical solution is known, in order to test the method.

In International Conference on Finite Volumes for Complex Applications.
Camilla Fiorini
Camilla Fiorini
Maîtresse de Conférences

My research interests include computational fluid dynamics, numerical analysis and PDEs.