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A critical evaluation of upstream differencing applied to problems involving fluid flow. (English) Zbl 0346.76064

76R10 Free convection
76D05 Navier-Stokes equations for incompressible viscous fluids
65N06 Finite difference methods for boundary value problems involving PDEs
Full Text: DOI
[1] Courant, R.; Isaacson, E.; Rees, M., On the solution of non-linear hyperbolic differential equations by finite differences, Comm. pure appl. math., 5, 243-255, (1952) · Zbl 0047.11704
[2] Torrance, K.E., Comparison of finite difference computations of natural convection, J. res. N.B.S., 72B, 281-301, (1968) · Zbl 0213.53802
[3] Roberts, K.V.; Weiss, N.O., Convective difference schemes, Math. comp., 20, 272-299, (1966) · Zbl 0137.33404
[4] Bozeman, J.D.; Dalton, C., Numerical study of viscous flow in a cavity, J. comp. phys., 12, 348-363, (1973) · Zbl 0261.76024
[5] de G. Allen, D.N.; Southwell, R.V., Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder, Q.J. mech. appl. math., 8, 129-145, (1955) · Zbl 0064.19802
[6] Spalding, D.B., A novel finite difference formulation for differential expressions involving both first and second derivatives, Int. J. numer. meth. eng., 4, 551-559, (1972)
[7] Raithby, G.D.; Torrance, K.E., Upstream-weighted schemes and their application to elliptic problems involving fluid flow, Computers and fluids, 2, 191-206, (1974) · Zbl 0335.76008
[8] Harlow, F.H.; Amsden, A.A., A numerical fluid dynamics calculation method for all flow speeds, J. comp. phys., 8, 197-213, (1971) · Zbl 0221.76011
[9] MacCormack, R.W.; Paullay, A.J., Computational efficiency achieved by time splitting of finite difference operators, AIAA paper, 72-154, (1972)
[10] Roache, P.J., Computational fluid dynamics, (1972), Hermosa, Publ Albuquerque, N.M · Zbl 0251.76002
[11] Roache, P.J., On artificial viscosity, J. comp. phys., 10, 169-184, (1972) · Zbl 0247.76035
[12] Hirt, C.W., Heuristic stability theory for finite difference equations, J. comp. phys., 2, 339-355, (1968) · Zbl 0187.12101
[13] Strong, A.B.; Schneider, G.E.; Yovanovich, M.M., Thermal constriction resistance of a disk with arbitrary heat flux — finite difference solution in oblate spheroidal coordinates, AIAA paper no. 74-690, (1974)
[14] Molenkamp, C.R., Accuracy of finite difference methods applied to the advection equation, J. appl. meteor., 7, 160-167, (1968)
[15] Fromm, J.E., Practical investigation of convective difference approximations of reduced dispersion, Phys. fluids supplement, II, 3-12, (1960) · Zbl 0207.25701
[16] Leith, C.E., Numerical simulation of the Earth’s atmosphere, Meth. comp. phys., 4, 1-28, (1965)
[17] Gosman, A.D.; Pun, W.M.; Runchal, A.K.; Spalding, D.B.; Wolfstein, M., Heat and mass transfer in recirculating flows, (1969), Academic Press New York · Zbl 0239.76001
[18] de Vahl Davis, G.; Mallinson, G.D., False diffusion in numerical fluid mechanics, () · Zbl 0262.65073
[19] Raithby, G.D., Skew-upstream differencing schemes for problems involving fluid flow, Comp. meth. appl. mech. eng., 9, 151-162, (1976) · Zbl 0347.76066
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