We have developed a refined model of coupled heat and fluid flow to numerically simulate off-axis hydrothermal circulation through the upper oceanic crust. The new representation includes mesh elements with curved sides and noncentered nodes. These curvilinear elements allow improved simulation of topography at the seafloor and within underlying sediment and basaltic layers. Curvilinear simulations of circulation at Deep Sea Drilling Project/Ocean Drilling Program site 504 confirm the broad conclusions derived from the rectilinear simulations of Fisher et al. (1990) but also suggest that permeability within the upper few hundred meters of crust around hole 504B must be concentrated within several narrow zones. This interpretation is consistent with core observations and wireline logs from hole 504B. Within these highly permeable zones, absolute permeability may be several orders of magnitude higher than the bulk permeability measured for the upper crust as a whole. A series of detailed parametric simulations was conducted to determine the quantitative importance of basal heat flow, seafloor bathymetry, basement relief, and differential sediment thickness in modifying the geometry and intensity of off-axis hydrothermal circulation. These studies reveal that basement relief and differential sediment thickness are more important than seafloor bathymetry in enhancing off-axis convection within the seafloor. Observed natural correlations between seafloor bathymetry and heat flow may exist because bathymetry is a proxy for the other two important parameters, basement relief and differential sediment thickness. Off-axis convection at geochemically significant velocities is possible even with heat input appropriate for some of the oldest oceanic crust. A thick sediment layer over older crust may cause enough conductive refraction at the seafloor to mask the variations in seafloor heat flow often associated with off-axis hydrothermal convection.