One and two dimensional inviscid and two dimensional viscid flow analysis using the kinetic energy preserving scheme

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Abstract

In this work, the Kinetic Energy Preserving (KEP) scheme -which is introduced recently by Jameson- has been investigated and compared to other artificial viscosity and upwind schemes. The discretization of the governing equations in the KEP scheme is performed in such a way that the total kinetic energy is conserved in all points with no shock. For the KEP method, there is no need to add any artificial dissipation in the region with low pressure gradient. The purpose of this study is to introduce a stable numerical method that enters a minimum artificial dissipation only in the vicinity of shocks. In this paper, an inviscid one-dimensional flow through a convergent-divergent nozzle, two-dimensional flow on a bump and a viscous two-dimensional flow with axial symmetry are considered. It is shown that the KEP scheme is more accurate if the number of mesh points is increased; and in contrast to other schemes, there is no limit in increasing the number of points.

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References

[1]  Jameson, A., “Formulation of Kinetic Energy Preserving Conservative Schemes for          Gas Dynamics and Direct Numerical Simulation of One-dimensional Viscous Compressible Flow in a Shock Tube using Entropy and Kinetic Energy Preserving Schemes”, Report ACL,  Vol. 34-2, pp. 188-208, (2008).
 
[2]  Jameson, A., “The Construction of Discretely Conservative Finite Volume Schemes that also Globally Conserve Energy or Entropy”, Report ACL, Vol. 34-2, pp.152-187, (2008).
 
[3]  Honein, A.E., and Moin, P., “Higher Entropy Conservation and Numerical Stability of Compressible Turbulence Simulations”, J. Comp. Phys., Vol. 201, pp. 531–545, (2004).
 
[4]  Jameson, A., “Energy Estimates for Nonlinear Conservation Law with Applications to Solutions of the Burgurs Equation and One-dimensional Viscous Flow in a Shock Tube by Central Difference Schemes”, 18th Computational Fluid Dynamics Conference by the AIAA, Miami, June 28, (2007).
 
[5]  Jameson, A., and Allaneu, Y., “Direct Numerical Simulations of Plunging Airfoils”, 48th Aerospace Sciences Meeting by the AIAA, Orlando, Florida, January 4-7, (2010).
 
[6]  Shu, C.W., “Total-variation-diminishing Time Discretizations”, SIAM J. Sci. Statist. Computing. Vol. 9, pp. 1073–1084, (1988).
 
[7]  Jameson, A., and Allaneu, Y., “Direct Numerical Simulations of a Two Dimensional Viscous Flow in a Shock Tube using a Kinetic Energy Preserving Schemes”, 19th Computational Fluid Dynamics Conference by the AIAA, San Antonio, Texas, June 22-25, (2009).
 
[8]  Jameson, A., Schmidt, W., and Turkel, E., “Numerical Solutions of the Euler Equations by Finite Volume Methods using Runge-Kutta Time-stepping Schemes”, AIAA 14th Fluid and Plasma Dynamic Conference, Palo Alto, (1981).
 
[9]  Swanson, R., and Turkel, E., “Artificial and Centeral Difference Schemes for the Euler and Navier Stokes Equations”, AIAA 8th Computations Fluid Dynamics Conference, New York, pp.55-69, (1986).
 
[10] Jameson, A., “Analysis and Design of Numerical Schemes for Gas Dynamics Artificial Diffusion, Upwind Biasing, Limiters and their Effect on Accuracy and Multigrid Convergence”, International Journal of Computational Fluid Dynamics, Vol. 4, pp. 171-218, (1995).
 
]11[  سالاری، م، "مقایسه و تحلیل طرح­های بالادست رو و طرح­های اتلاف مصنوعی"، پایان­نامه­ کارشناسی ارشد،  دانشگاه فردوسی مشهد، (1387).
 
[12] Eidelman, S., Colella, P., and Shreeve, R. P., “Applications of the Godunov Method and its Second-order Extension to Cascade Flow Modeling”, AIAA Journal, Vol. 22, pp. 1609-1615, (1984).
 
]13[علیدادی، م، "تحلیل عددی جریان دوبعدی و مغشوش حول یک پرتابه با اعمال مدل های تلاطمی"، پایان­نامه­ کارشناسی ارشد، دانشگاه فردوسی مشهد، (1380).
 
]14[شلختینگ، ه. ترجمه، مهرابیان، م. " نظریه ی لایه مرزی"، انتشارات دانشگاه شهید باهنرکرمان، (1384).
Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 14, Issue 4 - Serial Number 29
Fluid Mechanics and Heat Transfer
March 2012
Pages 93-117

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  • Receive Date: 12 October 2012
  • Accept Date: 12 October 2012

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