A time-splitting approach to solving the Navier-Stokes equations

Computers and Fluids

Volumn 25, Issue 4, 1996, Pages 421-431

  Batten, P ^a   Ingram, D M ^a   Saunders, R ^a   Causon, D M ^a  

^a MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBLE FLOW; DIFFUSION IN LIQUIDS; HEAT CONVECTION; INTEGRATION; NUMERICAL METHODS; PROBLEM SOLVING; UNSTEADY FLOW; VISCOUS FLOW;

CONVECTION DIFFUSION SPLITTING; DIFFUSION EQUATIONS; EULER SOLVER; SCALAR TRIDIAGONAL MATRIX INVERSIONS; TIME SPLITTING APPROACH; VISCOUS TIME STEP RESTRICTIONS;

NAVIER STOKES EQUATIONS;

CONVECTION; DIFFUSION; NAVIER-STOKES EQUATIONS;

EID: 0030131317     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7930(96)00003-5     Document Type: Article

References (18)

1. D. W. Peaceman and H. H. Rachford, The numerical solution of parabolic and elliptic differential equations. SIAM J. 53, (1955).
2. P. K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21, 995-1011 (1984).
3. N. N. Yanenko, The Method of Fractional Steps. Springer, New York (1971).
4. G. Strang, On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5, 506-517 (1968).
5. D. M. Causon, High resolution finite volume schemes and computational aerodynamics. In: 2nd Int. Conf. Hyperbolic Problems Aachen, Germany. Springer, Berlin (1988).
6. W. R. Briley and H. McDonald, Solution of the multidimensional compressible Navier-Stokes equations by a generalized implicit method. J. Comput. Phys. 24 (1976).
7. R. M. Beam and R. F. Warming, An implicit factored scheme for the compressible Navier-Stokes equations. AIAA J. 16 393 (1978).
8. R. W. MacCormack, An efficient numerical method for solving the time-dependent compressible Navier Stokes equations at high Reynolds number. AIAA Paper 75-1 (1976).
9. R. W. MacCormack and B. S. Baldwin, A numerical method for solving the Navier-Stokes equations with application to shock boundary-layer interaction. AIAA Paper 75-1 (1975).
10. R. W. MacCormack and A. J. Paullay, Computational efficiency achieved by time-splitting of finite difference operators. AIAA Paper 72-154 (1972).
11. R. E. Brown, Numerical solution of the two-dimensional unsteady Navier-Stokes equations using viscous-convective operator splitting. M.Sc. thesis, College of Aeronautics, Cranfield Institute of Technology, Cranfield (1990).
12. S. V. Patankar, Numerical Heat Transfer and Fluid Flow. Hemisphere, Washington, DC (1980).
13. M. O. Bristeau, R. Glowinski, J. Periaux and H. Viviand (Eds), Numerical simulation of compressible Navier-Stokes flows. In: Proc 1985 GAMM Workshop, Notes on Numerical Fluid Mechanics, Vol. 18 (1985).
14. B. Van Leer, Towards the ultimate conservative difference scheme II. Monotonicity and conservation combined in a second-order scheme. J. Comput. Phys. 14, 361-370 (1974).
15. A. Harten, P. D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. SIAM Rev. 25, 35-61 (1983).
16. C. J. Borland, Numerical prediction of the unsteady flow field in an open cavity. AIAA Paper 77-673 (1977).
17. J. E. Rossiter, Wind tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. RAE Technical report RAE-ARC-R&M 3438 (1966).
18. H. H. Heller, D. G. Holmes and E. E. Covert, Flow-induced pressure oscillations in shallow cavities. J. Sound Vibr. 18, (1971).