Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (4): 489-500.doi: https://doi.org/10.1007/s10483-018-2317-8

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Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles

S. M. H. KARIMIAN1, A. AMANI1, M. SEYEDNIA2   

  1. 1. Department of Aerospace Engineering, Amirkabir University of Technology, Tehran IR 15875-4413, Iran;
    2. Faculty of New Sciences and Technologies, University of Tehran, Tehran IR 14395-1561, Iran
  • 收稿日期:2017-07-12 修回日期:2017-10-26 出版日期:2018-04-01 发布日期:2018-04-01
  • 通讯作者: A. AMANI, E-mail:ahmad.amani@aut.ac.ir E-mail:ahmad.amani@aut.ac.ir

Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles

S. M. H. KARIMIAN1, A. AMANI1, M. SEYEDNIA2   

  1. 1. Department of Aerospace Engineering, Amirkabir University of Technology, Tehran IR 15875-4413, Iran;
    2. Faculty of New Sciences and Technologies, University of Tehran, Tehran IR 14395-1561, Iran
  • Received:2017-07-12 Revised:2017-10-26 Online:2018-04-01 Published:2018-04-01
  • Contact: A. AMANI E-mail:ahmad.amani@aut.ac.ir

摘要:

The computational cost of numerical methods in microscopic-scales such as molecular dynamics (MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.

关键词: Newton's interpolation formula, Newton's polynomial of a lot of centers, Newton's Theorem of a lot of centers, interpolation formula of the difference of higher order, computational cost, molecular dynamics (MD), symmetric boundary condition, nozzle argon flow

Abstract:

The computational cost of numerical methods in microscopic-scales such as molecular dynamics (MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.

Key words: Newtons interpolation formula, Newtons polynomial of a lot of centers, Newtons Theorem of a lot of centers, interpolation formula of the difference of higher order, computational cost, symmetric boundary condition, nozzle argon flow, molecular dynamics (MD)

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