Higher-Dimensional Deterministic Approach for Conservation Laws with Random Initial Data

We discuss random hyperbolic conservation laws and introduce a formulation interpreting the stochastic variables as additional spatial dimensions with zero flux. The approach is compared to established non–intrusive approaches for random conservation laws. For the numerical approximation a Runge–Kutta discontinuous Galerkin method is employed and a cellwise integration is used for the approximation of the stochastic moments. By means of grid adaptation the computational effort is reduced in the spatial as well as in the stochastic directions, simultaneously. Results on Burgers’ equation are validated by several numerical examples and compared to Monte Carlo simulations.