Direct Numerical Simulation of Supersonic and Transonic Compressible Viscous Flow by Kinetic Energy Preserving Scheme

علوم کاربردی و محاسباتی در مکانیک

Article 2, Volume 28, Issue 1 - Serial Number 15, March 2017, Pages 15-30   

Document Type: Original Article

DOI: 10.22067/fum-mech.v28i1.30888

Authors

saleh abbasi mood; Majid Malek Jafarian^*

Birjand

Abstract

Present paper investigates the numerical solution of two-dimensional unsteady compressible Navier-Stokes equations by a new scheme based on the finite volume method. Kinetic Energy Preserving (KEP) scheme is introduced for solving the supersonic and Transonic external compressible flow field on very fine grids (with a number of cells of the order of the Reynolds number) without artificial dissipation terms even in place of shock waves. It should be noted that the solution of flow field with this scheme in this range of speed, is presented for the first time. By discretization of the governing equations based on KEP scheme and elimination of dissipative effects, the Direct Numerical Simulation (DNS) of the flow is possible. The results of this solution for supersonic flow over flat plate and Transonic flow over the airfoil at low Reynolds numbers show that the KEP method can be presented stable and non-oscillatory solution by no artificial dissipation even in areas with shock waves. Therefore, the KEP method can be used for DNS of turbulent flows (without a modeling the turbulence phenomena itself).

Keywords

Compressible Viscous Flow; Finite Volume Method; Direct Numerical Simulation; Kinetic Energy Preserving Scheme

Supplementary Files

2-malekjafarian-EA.pdf

References

1. Chandrashekar, P., "Kinetic energy preserving and entropy stable finite volume schemes for compressible Euler and Navier-Stokes equations", TIFR Center for Applicable Mathematics, Bangalore, India, (2012).

2. 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", Aerospace Computing Laboratory, Report ACL 2007–2, Stanford University, (2007).

3. Allaneau, Y., Jameson, A., "Direct numerical simulations of a two dimensional viscous flow in a shock tube using a kinetic energy preserving schemes", 19th AIAA Computational Fluid Dynamics Conference, AIAA 2009-3797, San Antonio, Texas, June 22-25, (2009).

4. Allaneau, Y., Jameson, A., "Direct numerical simulations of plunging airfoils", 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA 2010-728, Orlando, Florida, January 4-7, (2010).

5. Allaneau, Y., Jameson, A., "Kinetic energy conserving discontinuous galerkin scheme", 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2011-198, Orlando, Florida, January 4-7 , (2011).

6. Swanson, R.C., Turkel, E., "On central difference and upwind scheme", J. Comp. Phys., 101, pp. 297- 306, (1992).

7. Anderson, J.D., "Computational Fluid Dynamics the Basics with Applications", McGraw-Hill, New York, (1995).

8. Mittal, S., "Finite element computation of unsteady viscous compressible flows", Journal of Computer Methods in Applied Mechanics and Engineering, No. 157, pp. 157-175, (1998).