We present a finite difference-(Multi-level) Monte Carlo algorithm to efficiently compute statistical solutions of the two dimensional Navier-Stokes equations, with periodic bound- ary conditions and for arbitrarily high Reynolds number. We propose a reformulation of statistical solutions in the vorticity-stream function form. The vorticity-stream function for- mulation is discretized with a finite difference scheme. We obtain a convergence ...

We describe a shock-capturing streamline diffusion space-time discontinuous Galerkin (DG) method to discretize the shallow water equations with variable bottom topography. This method, based on the entropy variables as degrees of freedom, is shown to be energy stable as well as well-balanced with respect to the lake at rest steady state. We present numerical experiments illustrating the numerical method.

Tunnelling delays is a hotly debated topic, with many conflicting definitions and little consensus on when and if such definitions accurately describe the physical observables. Here we relate these different definitions to distinct experimental observables in strong field ionization, finding that two definitions, Larmor time and Bohmian time, are compatible with the attoclock observable and the resonance lifetime of a bound state, ...