Abstract
Many fascinating astrophysical phenomena can be simulated insufficiently by standard numerical schemes for the compressible hydrodynamics equations. In the present work, a high performant 2D hydrodynamical code has been developed. The model is designed for the planetary formation that consists of momentum, continuity and energy equations. Since the two-phase model seems to be hardly executed, we will show in a simplified form, the implementation of this model in one-phase. It is applied to the Solar System that such stars can form planets. The finite volume method (FVM) is used in this model. We aim to develop a first-order well-balanced scheme for the Euler equations in the the radial direction, combined with second-order centered ux following the radial direction. This conception is devoted to balance the uxes, and guarantee hydrostatic equilibrium preserving. Then the model is used on simplified examples in order to show its ca- pability to maintain steady-state solutions with a good precision. Additionally, we demonstrate the performance of the numerical code through simulations. In particularly, the time evolution of gas orbited around the star, and some proper- ties of the Rossby wave instability are analyzed. The resulting scheme shows consequently that this model is robust and simple enough to be easily implemented.
Highlights
The Planetesimal formation is a complex problem due to great incomprehension process, in where stars of the Solar System form planets
The first planets observed outside the Solar System, indicated that planetesimal formation is possible around massive stars
Like our Sun, takes approximately 1 million years to form, with a protoplanetary disk that will evolve into a planetary system takes from 10 to 100 million years to form
Summary
The Planetesimal formation is a complex problem due to great incomprehension process, in where stars of the Solar System form planets. Our study was interested by authors of paper [11] (2003), who investigated the evolution of gravitationally unstable protoplanetary gaseous disks using smoothed-particle hydrodynamics (SPH). In they have applied numerical method (Lagrangian) for simulating the fluxes of a given fluid. They have applied numerical method (Lagrangian) for simulating the fluxes of a given fluid They meshed a physical demain in order to solve hydrodynamic equations. This article investigates a new numerical code for the Planetesimal formation This code models the flow of particles in disks with refined mesh.
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