The physics implemented in VINE as well as the numerical algorithms which have been used for the code are described in detail in these two papers:
Paper1 describes most of the implemented features (integrators, individual time step algorithm, SPH formulation, periodic boundaries,...) and includes several test cases.
Paper2 gives more details about the implementation of the tree structure and the parallelization strategy. It describes the optimizations and shows their effects on both the serial and parallel performance of VINE.