Context : Classical novae are explosive phenomena that take place in stellar binary systems . They are powered by mass transfer from a low-mass main sequence star onto a white dwarf ( either CO or ONe ) . The material accumulates for 10 ^ { 4 } -10 ^ { 5 } yr until ignition under degenerate conditions , resulting in a thermonuclear runaway . The nuclear energy released produces peak temperatures of \sim 0.1 - 0.4 GK . During these events , 10 ^ { -7 } -10 ^ { -3 } M _ { \odot } enriched in intermediate-mass elements ( with respect to solar abundances ) are ejected into the interstellar medium . However , the origin of the large metallicity enhancements and the inhomogeneous distribution of chemical species observed in high-resolution spectra of ejected nova shells is not fully understood . Aims : Recent multidimensional simulations have demonstrated that Kelvin-Helmholtz instabilities that operate at the core-envelope interface can naturally produce self-enrichment of the accreted envelope with material from the underlying white dwarf at levels that agree with observations . However , such multidimensional simulations have been performed for a small number of cases , and much of the parameter space remains unexplored . Methods : Here we investigate the dredge-up , driven by Kelvin-Helmholtz instabilities , for white dwarf masses in the range 0.8-1.25 M _ { \odot } and different core compositions ( CO-rich and ONe-rich substrates ) . We present a set of five numerical simulations performed in two dimensions aimed at analyzing the possible impact of the white dwarf mass ( and composition ) on the metallicity enhancement and on the explosion characteristics . Results : We observe greater mixing ( \sim 30 \% higher when measured in the same conditions ) , at the time we stop the simulations , and more energetic outbursts for ONe-rich substrates than for CO-rich substrates and for more massive white dwarfs . Conclusions :