Semi-conservative high order scheme with numerical entropy indicator for intrusive formulations of hyperbolic systems

This work considers high order discretizations for the intrusive stochastic Galerkin and polynomial moment method. Applications to hyperbolic systems result in solutions that typically involve a large number of wave interactions that must be resolved numerically. In order to reduce numerical oscillations, analytical and numerical entropy indicators are used to perform CWENO-type reconstructions in characteristic variables, when and where non-smooth solutions arise. The proposed method is analyzed for random isentropic Euler equations. In particular, a semi-conservative scheme is employed for non-polynomial pressure in order to reduce the computational cost, while still ensuring correct shock speeds.