High-Order Finite-Volume Methods for Hyperbolic PDEs with Uncertainties

The authors develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The methods are realized in the semi-discrete finite-volume framework and use fifth-order weighted essentially non-oscillatory (WENO) interpolations in the random space combined with second-order piecewise linear reconstruction in the physical space.