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 . The material piles up under degenerate conditions and a thermonuclear runaway ensues . The energy released by the suite of nuclear processes operating at the envelope heats the material up to peak temperatures of \sim ( 1 - 4 ) \times 10 ^ { 8 } K. During these events , about 10 ^ { -4 } -10 ^ { -5 } M _ { \sun } , enriched in CNO and other intermediate-mass elements , are ejected into the interstellar medium . To account for the gross observational properties of classical novae ( in particular , a metallicity enhancement in the ejecta above solar values ) , numerical models assume mixing between the ( solar-like ) material transferred from the companion and the outermost layers ( CO- or ONe-rich ) of the underlying white dwarf . Aims : The nature of the mixing mechanism that operates at the core-envelope interface has puzzled stellar modelers for about 40 years . Here we investigate the role of Kelvin-Helmholtz instabilities as a natural mechanism for self-enrichment of the accreted envelope with core material . Methods : The feasibility of this mechanism is studied by means of the multidimensional code FLASH . Here , we present a series of 9 numerical simulations perfomed in two dimensions aimed at testing the possible influence of the initial perturbation ( duration , strength , location , and size ) , the resolution adopted , or the size of the computational domain on the results . Results : We show that results do not depend substantially on the specific choice of these parameters , demonstrating that Kelvin-Helmholtz instabilities can naturally lead to self-enrichment of the accreted envelope with core material , at levels that agree with observations . Conclusions :