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We present the results of global 3-D MHD simulations of stratified andturbulent protoplanetary disc models. The aim of this work is to develop thindisc models capable of sustaining turbulence for long run times, which can beused for on-going studies of planet formation in turbulent discs. The resultsare obtained using two codes written in spherical coordinates: GLOBAL andNIRVANA. Both are time--explicit and use finite differences along with theConstrained Transport algorithm to evolve the equations of MHD. In the presenceof a weak toroidal magnetic field, a thin protoplanetary disc in hydrostaticequilibrium is destabilised by the magnetorotational instability (MRI). Whenthe resolution is large enough (25 vertical grid cells per scale height), theentire disc settles into a turbulent quasi steady-state after about 300 orbits.Angular momentum is transported outward such that the standard alpha parameteris roughly 4-6*10^{-3}. We find that the initial toroidal flux is expelled fromthe disc midplane and that the disc behaves essentially as a quasi-zero netflux disc for the remainder of the simulation. As in previous studies, the discdevelops a dual structure composed of an MRI--driven turbulent core around itsmidplane, and a magnetised corona stable to the MRI near its surface. Byvarying disc parameters and boundary conditions, we show that these basicproperties of the models are robust. The high resolution disc models we presentin this paper achieve a quasi--steady state and sustain turbulence for hundredsof orbits. As such, they are ideally suited to the study of outstandingproblems in planet formation such as disc--planet interactions and dustdynamics.Comment: 19 pages, 29 figures, accepted in Astronomy & Astrophysic

Global MHD simulations of stratified and turbulent protoplanetary discs