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  • 1
    Electronic Resource
    Electronic Resource
    A fully implicit direct Newton's method for the steady-state Navier-Stokes equationsWork performed under the auspices of the U.S. Dept. of Energy (DOE), Idaho Operations Office, under DOE Contract No. DE-AC07-76ID01570, the INEL Long Term Research Initiative in Computational Mechanics. (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 17 (1993), S. 449-461 
    Details
    ISSN: 0271-2091
    Keywords: Fully implicit ; Modified Newton's method ; Numerical Jacobian ; Mesh sequencing ; Navier-Stokes ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Newton's method and banded Gaussian elimination can be a CPU efficient method for steady-state solutions to two-dimensional Navier-Stokes equations. In this paper we look at techniques that increase the radius of convergence of Newton's method, reduce the number of times the Jacobian must be factored, and simplify evaluation of the Jacobian. The driven cavity and natural convection problems are used as test problems, and finite volume discretization is employed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650170602
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fully coupled finite volume solutions of the incompressible Navier-Stokes and energy equations using an inexact Newton method (1994)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 439-455 
    Details
    ISSN: 0271-2091
    Keywords: Incompressible Navier-Stokes ; Newton's method ; Conjugate gradient ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An inexact Newton method is used to solve the steady, incompressible Navier-Stokes and energy equation. Finite volume differencing is employed on a staggered grid using the power law scheme of Patankar. Natural convection in an enclosed cavity is studied as the model problem. Two conjugate-gradient -like algorithms based upon the Lanczos biorthogonalization procedure are used to solve the linear systems arising on each Newton iteration. The first conjugate-gradient-like algorithm is the transpose-free quasi-minimal residual algorithm (TFQMR) and the second is the conjugate gradients squared algorithm (CGS). Incomplete lower-upper (ILU) factorization of the Jacobian matrix is used as a right preconditioner. The performance of the Newton- TFQMR algorithm is studied with regard to different choices for the TFQMR convergence criteria and the amount of fill-in allowed in the ILU factorization. Performance data are compared with results using the Newton-CGS algorithm and previous results using LINPACK banded Gaussian elimination (direct-Newton). The inexact Newton algorithms were found to be CPU competetive with the direct-Newton algorithm for the model problem considered. Among the inexact Newton algorithms, Newton-CGS outperformed Newton- TFQMR with regard to CPU time but was less robust because of the sometimes erratic CGS convergence behaviour.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650190506
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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