565 RWTH Publication No: 841575        2021       
TITLE Description of random level sets by polynomial chaos expansions
AUTHORS Markus Bambach, Stephan Gerster, Michael Herty, Aleksey Sikstel
ABSTRACT We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulation is presented and proven hyperbolic. It induces a corresponding finite-volume scheme that is specifically taylored for uncertain velocities.
KEYWORDS Level sets, uncertainty quantification, Hamilton-Jacobi equations, hyperbolic conservation laws, stochastic Galerkin, finite-volume method
DOI 10.4310/CMS.2024.v22.n1.a4