Recent years have shown many advances in our knowledge of the collisional evolution of protoplanetary dust. Based on a variety of dust-collision experiments in the laboratory, our view of the growth of dust aggregates in protoplanetary disks is now supported by a deeper understanding of the physics involved in the interaction between dust agglomerates. However, the parameter space, which determines the collisional outcome, is huge and sometimes inaccessible to laboratory experiments. Very large or fluffy dust aggregates and extremely low collision velocities are beyond the boundary of today's laboratories. It is therefore desirable to augment our empirical knowledge of dust-collision physics with a numerical method to treat arbitrary aggregate sizes, porosities, and collision velocities. In this paper, we implement experimentally determined material parameters of highly porous dust aggregates into a smooth particle hydrodynamics (SPH) code, in particular an omnidirectional compressive-strength and a tensile-strength relation. We also give a prescription of calibrating the SPH code with compression and low-velocity impact experiments. In the process of calibration, we developed a dynamic compressive-strength relation and estimated a relation for the shear strength. Finally, we defined and performed a series of benchmark tests and found the agreement between experimental results and numerical simulations to be very satisfactory. SPH codes have been used in the past to study collisions at rather high velocities. At the end of this work, we show examples of future applications in the low-velocity regime of collisional evolution.