7e700ce4-379f-4de9-bc12-766cd315307820211020100408263naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mechanics1998-444810.46300/9104http://www.naun.org/cms.action?id=2828128202112820211510.46300/9104.2021.15https://www.naun.org/cms.action?id=23280TarikChakkourLGPM, CentraleSup´elec, Universit´e Paris-Saclay, Centre Europ´een de Biotechnologie et de Bio´economie (CEBB), 3 Rue des Rouges-Terres, 51110 Pomacle, FranceMany 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.102020211020202123324527https://www.naun.org/main/NAUN/mechanics/2021/a542003-027(2021).pdf10.46300/9104.2021.15.27https://www.naun.org/main/NAUN/mechanics/2021/a542003-027(2021).pdfS. Udry, D. 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