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 straight-forward. 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Komanduri, R., Chandrasekaran, N., and Raff, L. M. Molecular dynamic simulations of uniaxial tension at nanoscale of semiconductor materials for micro-electro-mechanical systems (MEMS) applications. Materials Science and Engineering: A, 340, 58–67 (2003)
Karniadakis, G. E., Beskok, A., and Aluru, N. Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York (2006)
Amani, A., Karimian, S. M. H., and Seyednia, M. A molecular dynamics study on the effects of wall-fluid interaction strength and fluid density on thermal resistance of graphene/argon interface. International Conference on Particle-Based Methods, Barcelona (2015)
Amani, A., Karimian, S. M. H., and Seyednia, M. A molecular dynamics simulation on the effect of different parameters on thermal resistance of graphene-argon interface. Molecular Simulation, 43, 276–283 (2016)
Travis, K. P., Todd, B. D., and Evans, D. J. Departure from Navier-Stokes hydrodynamics in confined liquids. Physical Review, 55, 4288–4295 (1997)
Bird, G. A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, Oxford (1994)
Ciofalo, M., Collins, M.W., and Hennessy, T. R. Modelling nanoscale fluid dynamics and transport in physiological flows. Medical Engineering and Physics, 18, 437–451 (1996)
Giordano, N. and Cheng, J. T. Microfluid mechanics: progress and opportunities. Journal of Physics Condensed Matter, 13, 271–295 (2001)
Alder, B. J. and Wainwright, T. E. Phase transition for a hard sphere system. Journal of Chemical Physics, 27, 1208–1209 (1957)
Rahman, A. Correlations in the motion of atoms in liquid argon. Physical Review A, 136, 405–411 (1964)
Rahman, A. and Stillinger, F. H. Molecular dynamics study of liquid water. Journal of Chemical Physics, 55, 3336–3359 (1971)
Ryckaert, J. P. and Bellemans, A. Molecular dynamics of liquid n-butane near its boiling point. Chememical Physics Letters, 30, 123–125 (1975)
McCammon, J. A., Gelin, B. R., and Karplus, M. Dynamics of folded proteins. nature, 267, 585–590 (1977)
Herman, J. and Berendsen, C. Bio-molecular dynamics comes of age. Science, 271, 954–955 (1996)
Deuflhard, P., Hermans, J., Leimkuhler, B., Mark, A. E., Reich, S., and Skeel, R. D. Computational Molecular Dynamics: Challenges, Methods, Ideas, Springer, Berlin, 21–24 (1997)
Taylor, V. E., Stevens, R. L., and Arnold, K. E. Parallel molecular dynamics: communication requirements for massively parallel machines. The Fifth Symposium on the Frontiers of Massively Parallel Computation, IEEE, 156–163 (1995)
Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. Journal of Computa-tional Physics, 117, 1–19 (1995)
Murty, R. and Okunbor, D. Efficient parallel algorithms for molecular dynamics simulations. Journal of Parallel Computing, 25, 217–230 (1999)
Freddolino, P. L., Arkhipov, A., Shih, A. Y., Yin, Y., Chen, Z., and Schulten, K. Application of Residue-Based and Shape-Based Coarse Graining to Biomolecular Simulations, Chapman and Hall/CRC Press, London (2008)
Tu, J. Y., Yeoh, G. H., and Liu, C. Q. Computational Fluid Dynamics: A Practical Approach (2nd ed.), Elsevier, 31–60 (2012)
Karimian, S. M. H. and Amani, A. A proposal for the implementation of symmetry boundary condition in molecular dynamics simulation. Proceedings of the Third European Conference on Microfluidics, Heidelberg (2012)
Karimian, S. M. H. and Izadi, S. Bin size determination for the measurement of mean flow velocity in molecular dynamics simulations. Proceedings of the Second European Conference on Microfluidics, Toulouse (2010)
Karimian, S. M. H., Izadi, S., and Farimani, A. B. A study on the measurement of mean veloc-ity and its convergence in molecular dynamics simulations. International Journal for Numerical Methods in Fluids, 67, 2130–2140 (2011)
Allen, M. P. and Tildesley, D. J. Computer Simulation of Liquids, Oxford University Press, Oxford (1989)
Haile, J. M. Molecular Dynamics Simulation, Elementary Methods (1st ed.), JohnWiley and Sons, New York (1997)
Rapaport, D. C. The Art of Molecular Dynamics Simulation (2nd ed.), Cambridge University Press, Cambridge (2004)
Hanasaki, I., Nakatani, A., and Kitagawa, H. Molecular dynamics study of Ar flow and He flow inside carbon nanotube junction as a molecular nozzle and diffuser. Science and Technology of Advanced Materials, 5, 107–113 (2004)
Verlet, L. Computer “experiments” on classical fluids I: thermo-dynamical properties of Lennard-Jones molecules. Physical Review, 159, 98–103 (1967)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Karimian, S.M.H., Amani, A. & Seyednia, M. Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles. Appl. Math. Mech.-Engl. Ed. 39, 489–500 (2018). https://doi.org/10.1007/s10483-018-2317-8
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-018-2317-8