An intrusive stochastic projection method for two-phase time-dependent flow subject to uncertainty is presented. Numerical experiments are carried out assuming uncertainty in the interface location, but the framework generalizes to uncertainty with known distribution in other input data. Uncertainty is represented through a truncated multiwavelet expansion.
We assume that the discontinuous features of the solution are restricted to subdomains in the computational domain and use a high-order method for the smooth regions coupled weakly through interfaces with a robust shock capturing method for the non-smooth regions.
The discretization of the non-smooth region is based on a generalization of the HLL flux, and have many properties in common with its deterministic counterpart. It is simple and robust, and captures the statistics of the shock. The discretization of the smooth region is carried out with high-order finite-difference operators satisfying a summation-by-parts property.
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