In the standard model of planetary formation, the formation of a Earth type planet, approximately at 1 A.U., starts at the final stage of evolution of a proto-star accretion disk. At the beginning, planetesimals of kilometer size are formed due to contact between them, without gravitational effects in the dust disk. Collisions among the planetesimals formed bodies of intermediate masses like asteroids and comets. The complete integration of the problem of creating an Earth size planet from kilometer size planetesimals using N body simulation will took approximately 10^12 bodies integrated for million of orbits, which is far of today computation capacity. Another way to perform these simulations is using the hydrodynamic approach, where the classical mass element representation can be done by the thermodynamics variables, as pressure, so that the movement can be affect by the position of the other particles, due to the pressure gradient, and also it is possible to treat collision as chocks of fluid elements which transform relative velocity into thermal energy. The Pencil Code is a high order code of finite difference used in compressible hydrodynamic flux with magnetic field. It is highly modular and can be easily adapted to different kinds of problems. In this work we will use The Pencil Code to simulate the formation of planetary embryos and understand how can be a good scenario for planetary formation.
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