Cross-validation of numerical schemes for extended hydrodynamical models of semiconductors

The numerical integration of the hydrodynamical model of semiconductors based on extended thermodynamics has been tackled. On account of the mathematical complexity of the system, no theoretical conditions of convergence are available for the existing schemes. Therefore in order to obtain numerical solution it was almost mandatory to resort to a cross-validation comparing the results given by two different methods. The kinetic scheme and the finite difference method represented by a suitable modification of the Nessyahu-Tadmor scheme furnish numerical results for the ballistic diode problem in good agreement even for non-smooth solutions.