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  • 1
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 525-544 
    ISSN: 0271-2091
    Schlagwort(e): Navier-Stokes ; Mixed formulation ; Orthomin ; Bi-CGSTAB ; Jacobi preconditioning ; SSOR ; Incomplete LU ; Inner iterations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: In the present paper, preconditioning of iterative equation solvers for the Navier-Stokes equations is investigated. The Navier-Stokes equations are solved for the mixed finite element formulation. The linear equation solvers used are the orthomin and the Bi-CGSTAB algorithms. The storage structure of the equation matrix is given special attention in order to avoid swapping and thereby increase the speed of the preconditioner. The preconditioners considered are Jacobian, SSOR and incomplete LU preconditioning of the matrix associated with the velocities. A new incomplete LU preconditioning with fill-in for the pressure matrix at locations in the matrix where the corner nodes are coupled is designed. For all preconditioners, inner iterations are investigated for possible improvement of the preconditioning. Numerical experiments are executed both in two and three dimensions.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 18 (1994), S. 1135-1151 
    ISSN: 0271-2091
    Schlagwort(e): Navier-Stokes ; Mixed formulation ; Bi-CGSTAB ; Incomplete LU ; Inner iterations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: In the present work a new iterative method for solving the Navier-Stokes equations is designed. In a previous paper a coupled node fill-in preconditioner for iterative solution of the Navier-Stokes equations proved to increase the convergence rate considerably compared with traditional preconditioners. The further development of the present iterative method is based on the same storage scheme for the equation matrix as for the coupled node fill-in preconditioner. This storage scheme separates the velocity, the pressure and the coupling of pressure and velocity coefficients in the equation matrix. The separation storage scheme allows for an ILU factorization of both the velocity and pressure unknowns. With the inner-outer solution scheme the velocity unknowns are eliminated before the resulting equation system for the pressures is solved iteratively. After the pressure unknown has been found, the pressures are substituted into the original equation system and the velocities are also found iteratively. The behaviour of the inner-outer iterative solution algorithm is investigated in order to find optimal convergence criteria for the inner iterations and compared with the solution algorithm for the original equation system. The results show that the coupled node fill-in preconditioner of the original equation system is more efficient than the coupled node fill-in preconditioner of the reduced equation system. However, the solution technique of the reduced equation system revals properties which may be advantageous in future solution algorithms.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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