  We discuss a non-equilibrium dynamical mean-field framework for simulating
inhomogeneous Hubbard models with local disorders. Our approach treats electron
interactions and disorders on equal footing, by considering only local
dynamical fluctuations. The theory reduces to non-equilibrium dynamical
mean-field theory in the presence of only electron-electron interactions and to
the coherent potential approximation in noninteracting systems with disorders.
Both time-dependent and steady-state problems are treated by implementing the
theory on the three branch Kadanoff-Baym contour and two-branch Keldysh
contour, respectively. Benchmarks on an $8$-site cube show that the method
yields rather accurate spectral functions in both the weakly and strongly
interacting regimes. In a cubic lattice, we demonstrate energy conservation
after an interaction quench and thermalization after just a few hopping times
in both clean and disordered systems. As an application, we study transport
through a serial double quantum-dot sandwiched between two leads, focusing on
the current and dot occupations after a voltage quench.
