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Numerical simulation of incompressible flows within simple boundaries. I: Galerkin (spectral) representations. (English) Zbl 0237.76012

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] Orszag, Numerical methods for the simulation of turbulence, Phys. Fluids (suppl. 2) 12 pp 250– (1969)
[2] Orszag, Transform method for the calculation of vector-coupled sums: application to the spectral form of the vorticity equation, J. Atmos. Sci. 27 pp 890– (1970) · doi:10.1175/1520-0469(1970)027<0890:TMFTCO>2.0.CO;2
[3] Patterson, Spectral calculations of isotropic turbulence: efficient removal of aliasing interactions, Phys. Fluids (1971) · Zbl 0225.76033 · doi:10.1063/1.1693365
[4] Orszag, Numerical simulation of incompressible flows within simple boundaries: accuracy, J. Fluid Mech. 49 pp 75– (1971) · Zbl 0229.76029 · doi:10.1017/S0022112071001940
[5] Taylor, Mechanism of the production of small eddies from large ones, Proc. Roy. Soc. 158 pp 499– (1937) · JFM 63.1358.03 · doi:10.1098/rspa.1937.0036
[6] Goldstein, Three-dimensional vortex motion in a viscous fluid, Phil. Mag. 30 pp 85– (1940) · JFM 66.1082.01 · doi:10.1080/14786444008520701
[8] Orszag, Galerkin approximations to flows within slabs, spheres, and cylinders, Phys. Rev. Letters 26 pp 1100– (1971) · doi:10.1103/PhysRevLett.26.1100
[9] Orszag, Accurate solution of the Orr-Sommerfeld equation, J. Fluid Mech. (1971) · Zbl 0237.76027 · doi:10.1017/S0022112071002842
[10] Galerkin, Rods and plates. Series occurring in various questions concerning the elastic equilibrium of rods and plates, Eng. Bull. (Vest. inzh.) 19 pp 897– (1971)
[11] Bubnov, Symposium of the Institute of Communication Engineers, No. 81 (1913)
[12] Fix, Fourier analysis of the finite element method in Ritz-Galerkin theory, Eng. Bull. (Vest. inzh.) 48 pp 265– (1969) · Zbl 0179.22501
[13] Orszag, Formulation of the theory of turbulence, Phys. Fluids 11 pp 43– (1968) · Zbl 0155.55801 · doi:10.1063/1.1691777
[14] Arakawa, Computational design for long-term numerical integration of the equations of motion: two-dimensional incompressible flow. Part 1, J. Comp. Phys. 1 pp 119– (1966) · Zbl 0147.44202 · doi:10.1016/0021-9991(66)90015-5
[15] Lax, Systems of conservation laws, Comm. Pure Appl. Math. 13 pp 217– (1960) · Zbl 0152.44802 · doi:10.1002/cpa.3160130205
[16] Molenkamp, Accuracy of finite-difference methods applied to the advection equation, J. Appl. Meteor. 7 pp 160– (1968) · doi:10.1175/1520-0450(1968)007<0160:AOFDMA>2.0.CO;2
[17] Phillips, The Atmosphere and the Sea in Motion pp 501– (1959)
[19] Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow (1963) · Zbl 0121.42701
[20] Lorenz, Maximum simplification of the dynamic equations, Tellus 12 pp 243– (1960) · doi:10.1111/j.2153-3490.1960.tb01307.x
[21] Ellsaesser, Evaluation of spectral versus grid methods of hemispheric numerical weather prediction, J. Appl. Meteor. 5 pp 246– · doi:10.1175/1520-0450(1966)005<0246:EOSVGM>2.0.CO;2
[22] Robert, Integration of a spectral barotropic model from 500-mb. charts, Mon. Weath. Rev. 96 pp 83– (1968) · doi:10.1175/1520-0493(1968)96<83:IOASBM>2.0.CO;2
[24] Stockham, Proc. AFIPS 1966 Spring Joint Computer Conference 29 pp 229– (1966)
[25] Cooley, Proc. IBM Scientific Computing Symposium on Digital Simulation of Continuous Systems pp 83– (1967)
[26] Cooley, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 pp 297– (1965) · Zbl 0127.09002 · doi:10.1090/S0025-5718-1965-0178586-1
[27] Cooley, The fast Fourier transform algorithm: programming considerations in the calculation of sine, cosine, and Laplace transforms, J. Sound Vib. 12 pp 315– (1970) · Zbl 0195.46301 · doi:10.1016/0022-460X(70)90075-1
[30] Lanczos, Applied Analysis (1956)
[31] Fox, Chebyshev Polynomials in Numerical Analysis (1968)
[32] Price, ”Error bounds for semidiscrete Galerkin approximations of parabolic problems with applications to petroleum reservoir mechanics,” in Numerical Solution of Field Problems in Continuum Physics, Amer. Math. Soc. pp 74– (1970) · Zbl 0218.76092
[33] Szegö, Orthogonal Polynomials, Amer. Math. Soc (1959)
[34] Swartz, Generalized finite-difference schemes, Math. Comp. 23 pp 37– (1969) · Zbl 0184.38502 · doi:10.1090/S0025-5718-1969-0239768-7
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