A numerical study of the axisymmetric couette-taylor problem using a fast high-resolution second-order central scheme

SIAM Journal on Scientific Computing

Volumn 20, Issue 3, 1998, Pages 858-877

  Kupferman, R A Z ^a  

^a LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

Central difference schemes; Couette taylor problem; Incompressible flow

Indexed keywords

CENTRAL DIFFERENCE SCHEME; COUETTE-TAYLOR PROBLEM; LINEAR STABILITY THEORY;

ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; INCOMPRESSIBLE FLOW; INTEGRATION; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; NEWTONIAN LIQUIDS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS;

NUMERICAL METHODS;

EID: 0032226451     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827597318009     Document Type: Article

References (27)

1. C.D. ANDERECK, S.S. Liu, AND H.L. SWINNEY, Flow regimes in a circular Couette system with independently rotating cylinders, J. Fluid Mech., 164 (1985), pp. 155-183.
2. J.B. BELL, P. COLELLA, AND H.M. GLAZ, A second order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85 (1989), pp. 257-283.
3. D.L. BROWN AND M.L. MINION, Performance of under-resolved two-dimensional incompressible flow simulations, J. Comput. Phys., 122 (1995), pp. 165-183.
4. S. CHANDRASEKHAR, Hydrodynamics and Hydromagnetic Stability, Dover, New York, 1961.
5. A.J. CHORIN, On the convergence of discrete approximations to the Navier-Stokes equations, Math. Comput., 22 (1969), pp. 745-762.
6. P. COLELLA AND E.G. PUCKETT, Modern Numerical Methods for Fluid Flow, in preparation.
7. P. COLELLA AND P. WOODWARD, The pieceuiise parabolic method (PPM) for gas-dynamical simulations, J. Comput. Phys., 54 (1984), pp. 174-201.
8. W. E AND C.-W. SHU, A numerical resolution study of high-order essentially non-oscillatory schemes applied to incompressible flow, J. Comput. Phys., 110 (1993), pp. 39-46.
9. S.K. GODUNOV, A finite difference method for the numerical computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb., 47 (1959), pp. 271-290.
10. E. GODLEWSKI AND P.-A. RAVIART, Hyperbolic Systems of Conservation Laws, Math. Appl., Ellipses, Paris, 1991.
11. A. HARTEN, ENO schemes with subcell resolution, J. Comput. Phys., 83 (1989), pp. 148-184.
12. G.S. JlANG AND E. TADMOR, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sei. Comput., in press.
13. R. KUPFERMAN, Simulation of Viscoelastic Fluids: Couette- Taylor flow, LBNL report 40302, Lawrence Berkeley National Laboratory, Berkeley, CA, 1997.
14. R. KUPFERMAN AND E. TADMOR, A fast high-resolution second-order central scheme for incompressible flows, Proc. Nat. Acad. Sei. U.S.A., 94 (1997), pp. 4848-4852.
15. P.D. LAX, Weak solutions of non-linear hyperbolic equations and their numerical computations, Comm. Pure Appl. Math., 7 (1954), pp. 159-193.
16. B. VAN LEER, Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method, J. Comput. Phys., 32 (1979), pp. 101-136.
17. R.J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhäuser-Basel, Switzerland, Verlag, 1992.
18. D. LEVY AND E. TADMOR, Non-oscillatory central schemes for the incompressible 2-D Euler equations, Math. Res. Lett., 4 (1997), pp. 1-20.
19. X.-D. Liu AND S. USHER, Nono s dilatory high order accurate self-similar maximum principle satisfying shock capturing. I., SIAM J. Numer. Anal., 33 (1996), pp. 760-779.
20. X.-D. Liu AND E. TADMOR, Third order nonoscillatory central scheme for hyperbolic conservation laws, Numer. Math., 79 (1998), pp. 397-425.
21. H. NESSYAHU AND E. TADMOR, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys., 87 (1990), pp. 408-463.
22. S. OSHER, Riemann solvers, the entropy condition, and difference approximations, SIAM J. Numer. Anal., 21 (1984), pp. 217-235.
23. LORD RAYLEIGH, On the dynamics of revolving fluids, Sei. Papers, 6 (1920), pp. 447-453.
24. P. ROE, Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43 (1981), pp. 357-372.
25. R. SANDERS AND A. WEISER, High resolution staggered mesh approach for nonlinear hyperbolic systems of conservation laws, J. Comput. Phys., 101 (1992), pp. 314-329.
26. P.K. SWEBY, High resolution schemes using flux limiters for hyperbolic conservation laws, SIAM J. Numer. Anal., 21 (1984), pp. 995-1011.
27. E. TADMOR AND C.C. Wu, Central scheme for the multidimensional MHD equations, in preparation.