We study the scaling behavior of domain-wall energies in two-dimensional Ising spin glasses with Gaussian and bimodal distributions of the interactions and different types of boundary conditions. The domain walls are generated by changing the boundary conditions at T=0 in one direction. The ground states of the original and perturbed system are calculated numerically by applying an efficient matching algorithm. Systems of size L x M with different aspect-ratios 1/8 <= L/M <= 64 are considered. For Gaussian interactions, using the aspect-ratio scaling approach, we find a stiffness exponent theta=-0.287(4), which is independent of the boundary conditions in contrast to earlier results. Furthermore, we find a scaling behavior of the domain-wall energy as predicted by the aspect-ratio approach. Finally, we show that this approach does not work for the bimodal distribution of interactions.
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