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A characteristic-based method for incompressible flows. (English) Zbl 0817.76058

Summary: A new characteristic-based method for the solution of the two-dimensional laminar incompressible Navier-Stokes equations is presented. For coupling the continuity and momentum equations, the artificial compressibility formulation is employed. The primitive variables (pressure and velocity components) are defined as functions of their values on the characteristics. The primitives variables on the characteristics are calculated by an upwind differencing scheme based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. The upwind scheme uses interpolation formulae of third-order accuracy. The time discretization is obtained by the explicit Runge-Kutta method. Validation of the characteristic-based method is performed on two different cases: the flow in a simple cascade and the flow over a backward-facing step.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Harlow, Phys. Fluids 8 pp 2182– (1965)
[2] Raithby, Numer. Heat Transfer 2 pp 417– (1979)
[3] Numerical Heat Transfer and Fluid Flow, Hemisphere, New York, 1980. · Zbl 0521.76003
[4] Chorin, J. Comput. Phys. 2 pp 12– (1967)
[5] Steger, AIAA J. 15 pp 581– (1977)
[6] and , Computational Methods for Fluid Flow, Springer, New York, 1983. · Zbl 0514.76001
[7] Rizzi, J. Fluid Mech. 153 pp 275– (1985)
[8] Choi, AAIA J. 23 pp 1519– (1985) · Zbl 0571.76016
[9] Kwak, AIAA J. 24 pp 390– (1986)
[10] and , ’Time accurate unsteady incompressible flow algorithms based on artifical compressibility’, AIAA Paper 87-1137, 1987.
[11] Hartwich, J. Fluids Eng. 110 pp 297– (1988)
[12] and , ’An upwind differencing scheme for the steady state incompressible Navier-Stokes equations, NASA TM 101051, 1988.
[13] Rogers, AIAA J. 28 pp 253– (1990)
[14] Dick, Int. J. numer. methods fluids 14 pp 1311– (1992)
[15] Michelassi, Int. J. numer. methods fluids 7 pp 1383– (1987)
[16] Computational Techniques for Fluid Dynamics, Vol. II, Springer, New York, 1983.
[17] Ramshaw, Comput. Fluids 20 pp 165– (1991)
[18] ’3d Euler calculations using characteristic flux extrapolation’, AIAA Paper 85-0119, 1985.
[19] ’Development of upwind numerical methods in high speed aerodynamics’, Ph.D. Thesis, National Technical University of Athens, 1993.
[20] Drikakis, Int. J. numer. methods fluids 12 pp 771– (1991)
[21] Drikakis, Appl. Math. Modell. 17 pp 282– (1993)
[22] and , ’Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes’, AIAA Paper 81-1259, 1981.
[23] Numerical Computation of Internal and External Flows, Vol. I, Wiley, Chichester, 1988.
[24] ’Characteristic flux averaging approach to the solution of Euler’s equations’, VKI Lecture Ser. 1987-04, 1987.
[25] and , Methoden der Mathematischen Physik I, Springer, Berlin, 1968. · Zbl 0156.23201
[26] ’High resolution upwind formulations for the Navier-Stokes equations’, VKI Lecture Ser. 1988-05, 1988.
[27] and , ’Implicit solution of the incompressible Navier-Stokes equations in primitive variables’, AAIA Paper 88-0717, 1988.
[28] Mansour, J Comput. Phys. 86 pp 147– (1990)
[29] Armaly, J. Fluid Mech. 127 pp 473– (1983)
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