Implementing Implicit Schemes in GENSMAC

C.M. Oishi, V.G. Ferreira, J.A. Cuminato, A. Castelo, M.F. Tomé, N. Mangiavacchi

Abstract


Implicit schemes are studied with the purpose of introducing them in the two-dimensional GENSMAC method, for the numerical solution of unsteady newtonian incompressible flows. By using the fractional-step approach, the Freeflow2D simulation system is employed to solve the conservation equations. The viscous terms in the Navier-Stokes equations are implicitly treated via the Implicit Backward (IR), Crank-Nicolson (CN) and Adams-Bashforth/Crank-Nicolson (AB/CN) schemes. The convective terms are explicitly treated by the upwind differencing Variable Order Non-Oscillatory Scheme (VONOS) scheme. For channel and impinging jet flows, the numerical techniques are robust and produce results that compare very well with the analytical solutions.

References


[1] A.A. Amsden and F.H. Harlow, A simplified MAC technique for incompressible fluid flow calculations, J. Comput. Phys., 6 (1970), 332-335.

V. Armenio, An improved MAC method (SIMAC) for unsteady high-Reynolds free surface flows, Int. J. Numer. Meth. Fluid, 24 (1997), 185-214.

G.K. Batchelor,“An Introduction to Fluid Dynamics”, Cambridge, 1970.

W.R. Briley and H. McDonald, An overview and generalization of implicit Navier-Stokes algorithms and approximate factorization, Comput. & Fluid, 30 (2001), 807-828.

A.F. Castelo, M.F. Tomé, J.A. Cuminato, M.L. Cesar and S. McKee, Freeflow: An intregated simulation system for three-dimensional free surface flows, Journal of Comp. and Visual. in Sci., 2 (2000), 199-210.

A.F. Castelo, M.F. Tomé, J.A. Cuminato, J. Oliveira, N. Mangiavacchi, V.G. Ferreira and S. McKee, Surface tension implemention for GENSMAC2D, Revista Brasileira de Ciências Mecânicas, XXIII (2001), 523-532.

H. Chattopadhyay and S.K. Saha, Turbulent flow and heat transfer from a slot jet impinging on a moving plate, (2003), in preparation.

J.J. Douglas and D.W. Peaceman, On the numerical solution of heat conduction problems in two and three space variable, Trans. Am. Math. Soc., 82 (1960), 421-439.

V.G. Ferreira, M.F. Tomé, N. Mangiavacchi, A. Castelo, J.A. Cuminato and S. McKee, High order upwinding and the hydraulic jump, Int. J. Numer. Meth. Fluid, 39 (2002), 549-583.

W. Hackbush, “Iterative Solution of Large Sparse System of Equations”, Springer-Verlag, New York, 1994.

F.H. Harlow and J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids, 8 (1965), 2182-2189.

K. Kim, S.J. Baek and H.J. Sung, An implicit velocity decoupling procedure for the incompressible Navier-Stokes equations, Int. J. Numer. Meth. Fluid, 38 (2002), 125-138.

J. Kim and P. Moin, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59 (1985), 308-323.

R. Peyret and T.D. Taylor, “Computional Methods for Fluid Flow”, Series in Computional Physics, Springer-Verlag, New York, 1983.

D.W. Peaceman and H.H. Rachford, The numerical solution of parabolic and elliptic diferential equations, J. Soc. Indust. Appl. Math, 3 (1955), 28-41.

M.F. Tomé and S. McKee, GENSMAC: A computational marker-and-cell method for free surface flows in general domains, J. Comput. Phys., 110 (1994), 171-186.

M.F. Tomé, A.F. Castelo, J. Murakami, J.A. Cuminato, R. Minghim, C.F. Oliveira, N. Mangiavacchi and S. McKee, Numerical simulation of axisymmetric free surface flows, J. Comput. Phys., 157 (2000), 441-472.

S. Turek, A comparative study of some time-stepping techniques for the incompressible Naveir-Stokes equations: From fully implicit nonlinear schems to semi-implicit projection methods, (2002), in preparation.

A. Varonos and G. Bergeles, Development and assessment of a variable-order non-oscillatory for convection term discretization, Int. J. Numer. Meths Fluids, 26 (1998), 1-16.

E.J. Watson, The radial spread of a liquid jet over a horinzontal plane, J. Fluid Mechs., 20 (1964), 481-499.




DOI: https://doi.org/10.5540/tema.2004.05.02.0259

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