Understanding how accretion proceeds in proto-planetary discs and more generally their dynamics is a crucial issue for explaining the conditions in which planets form. The role that accretion of gas from the surrounding molecular cloud onto the disc may have on its structure needs to be quantified. We perform tri-dimensional simulations using the Cartesian AMR code RAMSES of an accretion disc subject to infalling material. For the aspect ratio of $H/R simeq 0.15$ and disk mass $M_d simeq 10^{-2}$ M$_odot$ used in our study, we find that for typical accretion rates on the order of a few 10$^{-7}$ M$_odot$ yr$^{-1}$, values of the $alpha$ parameter as high as a few 10$^{-3}$ are inferred. The mass that is accreted in the inner part of the disc is typically at least $50%$ of the total mass that has been accreted onto the disc. Our results suggest that external accretion of gas at moderate values, onto circumstellar discs may trigger prominent spiral arms, reminiscent of recent observations made with various instruments, and lead to significant transport through the disc. If confirmed from observational studies, such accretion may therefore influence disc evolution.
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