scholarly journals Application of Two-dimensional Finite Volume Method to Protoplanetary Disks

2021 ◽  
Vol 15 ◽  
pp. 233-245
Author(s):  
Tarik Chakkour

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.

2011 ◽  
Vol 6 (3) ◽  
pp. 401-423 ◽  
Author(s):  
Stefan Berres ◽  
◽  
Ricardo Ruiz-Baier ◽  
Hartmut Schwandt ◽  
Elmer M. Tory ◽  
...  

2020 ◽  
Vol 213 ◽  
pp. 104715
Author(s):  
Rihua Yang ◽  
Heng Li ◽  
Aiming Yang

2020 ◽  
Vol 72 (10) ◽  
pp. 1303-1309
Author(s):  
Wenbin Gao ◽  
Weifeng Huang ◽  
Tao Wang ◽  
Ying Liu ◽  
Zhihao Wang ◽  
...  

Purpose By modeling and analyzing the two-phase mechanical seal of the fan-shaped groove end face, which is prone to phase change, an effective method to study the flow field of the mechanical seal when both cavitation and boiling exist simultaneously is found. Design/methodology/approach Based on the finite volume method, a fluid model was developed to investigate a two-phase mechanical seal. The validity of the proposed model was verified by comparing with some classical models. Findings By modeling and analyzing the two-phase mechanical seal of the fan-shaped groove end face, which is prone to phase change, the analysis of the gap flow field of the mechanical seal was realized when cavitation and boiling existed simultaneously. Originality/value Based on the model proposed for different conditions, the pressure and phase states in the shallow groove sealing gap were compared. The phase change rate between the mechanical seal faces was also investigated. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2019-0537/


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