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Cataclysmic Variables (CVs) and Symbiotic Binaries are close (or not so close) binary star systems which contain both a white dwarf (WD) primary and a larger cooler secondary star that typically fills its Roche Lobe. The cooler star is losing mass through the inner Lagrangian point of the binary and a fraction of this material is accreted by the WD. Here we report on our hydrodynamic studies of the thermonuclear runaway (TNR) in the accreted material that ends in a Classical Nova explosion. We have followed the evolution of the TNRs on both carbon-oxygen (CO) and oxygen-neon (ONe) WDs. We report on 3 studies in this paper. First, simulations in which we accrete only solar matter using NOVA (our 1-D, fully implicit, hydro code). Second, we use MESA for similar studies in which we accrete only Solar matter and compare the results. Third, we accrete solar matter until the TNR is ongoing and then switch the composition in the accreted layers to a mixed composition: either 25% WD and 75% solar or 50% WD and 50% Solar matter. We find that the amount of accreted material is inversely proportional to the initial 12C abundance (as expected). Thus, accreting solar matter results in a larger amount of accreted material to fuel the outburst; much larger than in earlier studies where a mixed composition was assumed from the beginning of the simulation. Our most important result is that all these simulations eject significantly less mass than accreted and, therefore, the WD is growing in mass toward the Chandrasekhar Limit.