Using cosmological simulations with a dynamic range in excess of 10 ^ { 7 } , we study the transport of gas mass and angular momentum through the circumnuclear region of a disk galaxy containing a supermassive black hole ( SMBH ) . The simulations follow fueling over relatively quiescent phases of the galaxy ’ s evolution ( no mergers ) and without feedback from active galactic nuclei ( AGNs ) , as part of the first stage of using state-of-the-art , high-resolution cosmological simulations to model galaxy and black hole co-evolution . We present results from simulations at different redshifts ( z = 6 , 4 , and 3 ) and three different black hole masses ( 3 \times 10 ^ { 7 } , 9 \times 10 ^ { 7 } , and 3 \times 10 ^ { 8 } \mbox { M } _ { \sun } ; at z = 4 ) , as well as a simulation including a prescription that approximates optically thick cooling in the densest regions . The interior gas mass throughout the circumnuclear disk shows transient and chaotic behavior as a function of time . The Fourier transform of the interior gas mass follows a power law with slope -1 throughout the region , indicating that , in the absence of the effects of galaxy mergers and AGN feedback , mass fluctuations are stochastic with no preferred timescale for accretion over the duration of each simulation ( \sim 1 - 2 \mbox { Myr } ) . The angular momentum of the gas disk changes direction relative to the disk on kiloparsec scales over timescales less than 1 \mbox { Myr } , reflecting the chaotic and transient gas dynamics of the circumnuclear region . Infalling clumps of gas , which are driven inward as a result of the dynamical state of the circumnuclear disk , may play an important role in determining the spin evolution of an SMBH , as has been suggested in stochastic accretion scenarios .