The stability of the accretion disk is solved by numerical simulations when the radial and azimuthal perturbations are considered, where we adopt the anomalous viscosity model, which is close to real accretion disks. The results are discussed in the inner, intermediate, and outer regions of the accretion disk, respectively. With the increase of viscosity, ␣, the thermal mode and the viscous mode, as well as the acoustic modes, become more unstable in the disk dominated by radiation pressure (inner region). The instability is also influenced by the azimuthal perturbation wavenumber, n. With the increase of n, the thermal mode becomes more unstable, while the in-mode and out-mode become more stable no matter if the disk is dominated by radiation pressure or by gas pressure (intermediate and outer regions). There are many differences between our results and others' results, especially in the inner region of the disk, when the anomalous viscosity is considered. PACS Nos.: 97.10.Gz, 94.30.Gm, 66.20.+d, 52.35.Ra.Résumé : Nous solutionnons par simulation numérique le problème de stabilité du disque d'accrétion en tenant compte des perturbations radiales et azimutales, tout en adoptant un modèle anomal de viscosité qui est proche des vrais disques d'accrétion. Avec l'augmentation de la viscosité ␣, les modes thermique et visqueux, aussi bien que les modes acoustiques, deviennent plus instables dans le disque dominé par la pression de radiation (région interne). L'instabilité est aussi influencée par le nombre d'onde n de la perturbation azimutale. Sous l'augmentation de n, le mode thermique devient plus instable, alors que les modes in et out deviennent plus stables dans un disque dominé par la pression de radiation ou du gaz (région intermédiaire et région externe). Il y a plusieurs différences entre nos résultats et ceux d'autres auteurs, spécialement dans la région interne du disque où on envisage la viscosité anomale. [Traduit par la Rédaction]
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