Hybrid methods in planetesimal dynamics (I) : Description of a new   composite algorithm
  The formation and evolution of protoplanetary systems, the breeding grounds of planet formation, is a complex dynamical problem that involves many orders of magnitudes. To serve this purpose, we present a new hybrid algorithm that combines a Fokker-Planck approach with the advantages of a pure direct-summation N-body scheme, with a very accurate integration of close encounters for the orbital evolution of the larger bodies with a statistical model, envisaged to simulate the very large number of smaller planetesimals in the disc. Direct-summation techniques have been historically developped for the study of dense stellar systems such as open and globular clusters and, within some limits imposed by the number of stars, of galactic nuclei. The number of modifications to adapt direct-summation N-body techniques to planetary dynamics is not undemanding and requires modifications. These include the way close encounters are treated, as well as the selection process for the "neighbour radius" of the particles and the extended Hermite scheme, used for the very first time in this work, as well as the implementation of a central potential, drag forces and the adjustment of the regularisation treatment. For the statistical description of the planetesimal disc we employ a Fokker-Planck approach. We include dynamical friction, high- and low-speed encounters, the role of distant encounters as well as gas and collisional damping and then generalise the model to inhomogenous discs. We then describe the combination of the two techniques to address the whole problem of planetesimal dynamics in a realistic way via a transition mass to integrate the evolution of the particles according to their masses. 
Patrick Glaschke, Pau Amaro-Seoane and Rainer Spurzem
astro-ph.EP astro-ph.GA