We have used molecular dynamics (MD) simulation to investigate ionic self-diffusivity in NaAlSi2O6 melts and glasses at pressures of 3 - 58 GPa and temperatures of 2500 - 5000 K, to evaluate the effectiveness of a two-body potential in reproducing pressure and temperature dependence of tracer self-diffusivities. For each species, self-diffusivity increased with increasing temperature; with increasing pressure up to similar to 15 GPa, the self-diffusivity of O, Si, and Al increased, while mobility of Na decreased. An Arrhenian fit to self-diffusivity data collected from simulations at temperatures above the kinetic glass transition (up to 15 GPa) gives: [GRAPHICS] for activation energy (E(a)) and activation volume (V-a). The MD-derived E(a,O) and V-a,V-O agree with laboratory results of 275 +/- 10 kJ/mol and -6.2 +/- 0.6 cm(3)/mol for E(a,O) and V-a,V-O respectively [Shimizu and Kushiro, 1984] measured in experiments at 1673 to 1923 K and 0.5 to 2 GPa. Agreement with the pre-exponential factor (D*) is poorer, with MD result of similar to 10(-6.6) for O and laboratory value similar to 10(-4.7). From similar to 15 GPa -25 GPa, V-a is similar to 0 m(3)/mol for O, Si, and Al; these species have a positive V-a for pressures above 25 GPa (V-a,V-O is similar to +1 cm(3)/mol). For pressures similar to 15 GPa the majority of the network cations are in 5- or 6- fold coordination, and more than 20% of the O is in 3-fold coordination. With increasing pressure, 4-fold Si and Al decrease monotonically, while 6-fold Si and Al increase monotonically. Pentahedral Si and Al maximize at nearly the same pressure as O self-diffusivity.