We obtain the strong precompactness of a family of solutions to a suitable regularization of multidimensional scalar conservation law via vanishing nonlinear diffusion and linear dispersion. We consider the flux which depends on the time and space variables, and obtain condition $\delta=O(\varepsilon^2)$, $\varepsilon\to0$, for the existence of a weak entropy solution. In comparison to known results for heterogeneous media (cf. [4]), our condition is weaker, thus more general.