A realizable filtered intrusive polynomial moment method

Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, challenging task is preserve hyperbolicity gPC moment system. An intrusive method guarantees polynomial (IPM) method, performs expansion on entropy variables. The while still being subject oscillations, requires solving convex optimization problem in every spatial cell and time step. aim this work mitigate IPM solution by applying filters. Filters reduce damping high order coefficients. Naive filtering, however, may lead unrealizable moments, means that does not have breaks down. In paper, we propose analyze two separate strategies guarantee existence problem. First, filter maintains realizability constructed from an underlying Fokker–Planck equation. Second, regularize be able cope with non-realizable Consequently, standard filters can applied regularized method. We demonstrate numerical results investigating Euler equations uncertain shock structures one- two-dimensional settings. are show proposed