Context : Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries .

Aims : Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions .

Methods : Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos .
Open ( vertical-field ) and closed ( perfect-conductor ) boundary conditions are used for the magnetic field .
The shear flow is such that the contours of shear are vertical , crossing the outer surface , and are thus ideally suited for driving a shear-induced magnetic helicity flux .

Results : We find that for given shear and rotation rate , the growth rate of the magnetic field is larger if open boundary conditions are used .
The growth rate first increases for small magnetic Reynolds number , { Rm } , but then levels off at an approximately constant value for intermediate values of { Rm } .
For large enough { Rm } , a small-scale dynamo is excited and the growth rate of the field in this regime increases as { Rm } ^ { 1 / 2 } .
Regarding the nonlinear regime , the saturation level of the energy of the total magnetic field is independent of { Rm } when open boundaries are used .
In the case of perfect conductor boundaries , the saturation level first increases as a function of { Rm } , but then decreases proportional to { Rm } ^ { -1 } for { Rm } \ga 30 , indicative of catastrophic quenching .
These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used .
The horizontally averaged mean field is still weakly decreasing as a function of { Rm } even for open boundaries .

Conclusions :