ON THE SENSITIVITY OF THE NONLINEAR TERM IN THE OUTFLOW BOUNDARY CONDITION
DOI:
https://doi.org/10.14311/AP.2021.61.0117Keywords:
Navier-Stokes equations, natural outlet boundary condition, finite volume methodAbstract
This paper studies the artificial outflow boundary condition for the Navier-Stokes system. This type of condition is widely used and it is therefore very important to study its influence on a numerical solution of the corresponding boundary-value problem. We particularly focus on the role of the coefficient in front of the nonlinear term in the boundary condition on the outflow. The influence of this term is examined numerically, comparing the obtained results in a close neighbourhood of the outflow. The numerical experiment is carried out for a fluid flow through the channel with so called sudden extension. Presented numerical results are obtained by means of the OpenFOAM toolbox. They confirm that the kinetic energy of the flow in the channel can be controlled by means of the proposed boundary condition.
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M. Feistauer, T. Neustupa. On Non-Stationary Viscous Incompressible Flow Through a Cascade of Profiles. Mathematical Methods in the Applied Sciences 29(16):1907–1941, 2006. doi:10.1002/mma.755.
M. Feistauer, T. Neustupa. On Some Aspects of Analysis of Incompressible Flow through Cascades of Profiles. In Operator Theoretical Methods and Applications to Mathematical Physics, vol. 147, pp. 257–276. Birkhäuser Basel, 2004. doi:10.1007/978-3-0348-7926-2_29.
M. Feistauer. Mathematical Methods in Fluid Dynamics. Longman Scientific & Technical, 1993.
S.I. Abdelsalam. M.M Bhatti. The Study of Non-Newtonian Nanofluid with Hall and Ion Slip
Effects on Peristaltically Induced Motion in a Non-uniform Channel. RSC Advances 8(15):7904–7915, 2018. doi:10.1039/C7RA13188G.
Y. Abd elmaboud, S.I. Abdelsalam, K.S. Mekheimer Couple Stress Fluid Flow in a Rotating Channel with Peristalsis. Journal of Hydrodynamics 30:307–316, 2018. doi:10.1007/s42241-018-0037-2.
S. S. Motsa, I. L. Animasaun Bivariate Spectral Quasi-linearisation Exploration of Heat Transfer in the Boundary Layer Flow of Micropolar Fluid with Strongly Concentrated Particles over a Surface at Absolute Zero due to Impulsive. International Journal of Computing Science and Mathematics 9:455–473, 2018. doi:10.1504/IJCSM.2018.10016504.
O. K. Koriko, I. L. Animasaun New Similarity Solution of Micropolar Fluid Flow Problem over an Uhspr in the Presence of Quartic Kind of Autocatalytic Chemical Reaction Frontiers in Heat and Mass Transfer 8, 2017. doi:10.5098/hmt.8.26.
O. K. Koriko, A.J. Omowaye, I. L. Animasaun, M. E. Bamisaye Melting Heat Transfer and Induced-Magnetic Field Effects on the Micropolar Fluid Flow towards Stagnation Point: Boundary Layer Analysis International Journal of Engineering Research in Africa 29:10–20, 2017. doi: 10.4028/www.scientific.net/JERA.29.10.
J. G. Heywood, R. Rannacher, S. Turek. Artificial Boundaries and Flux and Pressure Conditions for the Incompressible Navier-Stokes Equations. International Journal for Numerical Methods in Fluids 22(5):325–352, 1996. doi:10.1002/(sici)1097- 0363(19960315)22:5<325::aid-fld307>3.0.co;2-y.
R. Glowinski. Numerical Methods for Nonlinear Variational Problems. Springer, 1984.
C.-H. Bruneau, P. Fabrie. New Efficient Boundary Conditions for Incompressible Navier-Stokes Equations: A Well-Posedness Result. Mathematical Modelling and Numerical Analysis 30(7):815–840, 1996. doi:10.1051/m2an/1996300708151.
M. Braack, P. B. Mucha. Directional Do-Nothing Condition for the Navier-Stokes Equations. Journal of Computational Mathematics 32(5):507–521, 2014. doi:10.4208/jcm.1405-m4347.
T. Neustupa. A Steady Flow through a Plane Cascade of Profiles with an Arbitrarily Large Inflow: The Mathematical Model, Existence of a Weak Solution. Applied Mathematics and Computation 272:687–691, 2016. doi:10.1016/j.amc.2015.05.066.
H. G. Weller, G. Tabor, H. Jasak, C. Fureby. A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques. Computers in Physics 12(6):620–631, 1998. doi:10.1063/1.168744.
J. H. Ferziger, M. Peric. Computational Methods for Fluid Dynamics. Springer, 3rd edn., 2002.
F. Moukalled, L. Mangani, M. Darwish. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM and Matlab. Springer, 2016.
O. Winter, P. Svácek. On Numerical Simulation of Flexibly Supported Airfoil in Interaction with Incompressible Fluid Flow using Laminar-Turbulence Transition Model. Computers & Mathematics with Applications 2020. doi:10.1016/j.camwa.2019.12.022.
T. Bodnár, P. Fraunié. Artificial Far-Field Pressure Boundary Conditions for Wall-Bounded Stratified Flows. In Topical Problems of Fluid Mechanics 2018. Institute of Thermomechanics, AS CR, v.v.i., 2018. doi:10.14311/tpfm.2018.002.
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