Two-dimensional (2-D) modelling of dynamic seismic rupture is performed using a recent staggered-grid finite-difference formulation. Rupture boundary conditions are applied only inside the crack, without assuming any symmetry with respect to the rupture surface. By a simple rotation of the stress tensor, the local orientation of the crack is taken into consideration at each stress point. The grid size is controlled by the source discretization. The greater the number of grid nodes discretizing the finite source, the lower the grid size could be. Below the lower bound value associated with a given discretization, numerical artefacts are not negligible with respect to the spatial frequency content of the dynamic solution. Solutions converge for both point and finite sources by densifying the number of stress points in the source. Numerical scaling of boundary conditions is an important element of this convergence and allows the removal of high-frequency spurious effects of dynamic rupture conditions. For the self-similar crack, a comparison with Kostrov's analytical solution shows that accurate stress singularities are obtained for various crack orientations with respect to the numerical grid. For spontaneous rupture modelling assuming a slip-weakening constitutive law, similar solutions are found for both rupture kinematics and excited wavefield in planar faults with any orientation. Finally, based on these results, rupture propagation over an arbitrary non-planar fault is justified and then performed in the presence of heterogeneous medium.