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  • 1
    Electronic Resource
    Electronic Resource
    Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test (1997)
    Springer
    Computational mechanics 20 (1997), S. 46-52 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Rapid Crack Propagation (RCP) along pressurised plastic pipes is by far the most dangerous pipe failure mode. Despite the economic benefits offered by increasing pipe size and operating pressure, both strategies increase the risk and the potential consequences of RCP. It is therefore extremely important to account for RCP in establishing the safe operational conditions. Combined experimental-numerical study is the only reliable approach of addressing the problem, and extensive research is undertaken by various fracture groups (e.g. Southwest Research Institute – USA, Imperial College – UK). This paper presents numerical results from finite volume modelling of full-scale test on medium density polyethylene gas pressurised pipes. The crack speed and pressure profile are prescribed in the analysis. Both steady-state and transient RCPs are considered, and the comparison between the two shown. The steady-state results are efficiently achieved employing a full multigrid acceleration technique, where sets of progressively finer grids are used in V-cycles. Also, the effect of inelastic behaviour of polyethylene on RCP results is demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050215
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  • 2
    Electronic Resource
    Electronic Resource
    Application of the finite volume method to the analysis of dynamic fracture problems (1994)
    Springer
    International journal of fracture 66 (1994), S. 357-371 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A detailed description of a new numerical method for the solution of dynamic fracture problems is presented. The method employs finite volume discretization of the equilibrium equations. The present work considers the analysis of rapid crack propagation (RCP) in two-dimensional geometries only. The simulation of steady-state RCP in a peeling-strip geometry, and an economical approach which allows the calculation of the crack driving force from a ‘snapshot’ computation of the displacement field are described. Also presented is the modelling of transient RCP in single edge notch tensile specimens, based on a fixed-mesh ‘node release’ technique and a ‘holding back’ force concept. It is shown that finite volume results are in very good agreement with both analytical and finite element predictions. The accuracy, simplicity and efficiency of this novel method are also demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00018439
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  • 3
    Electronic Resource
    Electronic Resource
    Space conservation law in finite volume calculations of fluid flow (1988)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 8 (1988), S. 1037-1050 
    Details
    ISSN: 0271-2091
    Keywords: Space Conservation ; Numerical Calculation ; Fluid Flow ; 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: In the numerical solutions of fluid flow problems in moving co-ordinates, an additional conservation equation, namely the space conservation law, has to be solved simultaneously with the mass, momentum and energy conservation equations. In this paper a method of incorporating the space conservation law into a finite volume procedure is proposed and applied to a number of test cases. The results show that the method is efficient and produces accurate results for all grid velocities and time steps for which temporal accuracy suffices. It is also demonstrated, by analysis and test calculations, that not satisfying the space conservation law in a numerical solution procedure introduces errors in the form of artificial mass sources. These errors can be made negligible only by choosing a sufficiently small time step, which sometimes may be smaller than required by the temporal discretization accuracy.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650080906
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  • 4
    Electronic Resource
    Electronic Resource
    Fluid flow and heat transfer test problems for non-orthogonal grids: Bench-mark solutions (1992)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 329-354 
    Details
    ISSN: 0271-2091
    Keywords: Finite volume ; Multigrid ; Non-orthogonal grid ; Numerical accuracy ; Bench-mark solutions ; 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: Four problems of fluid flow and heat transfer were designed in which non-orthogonal, boundary-fitted grids were to be used. These are proposed to serve as test cases for testing new solution methods. This paper presents solutions of the test problems obtained by using a multigrid finite volume method with grids of up to 320 × 320 control volumes. Starting from zero fields, iterations were performed until the sum of the absolute residuals had fallen seven orders of magnitude, thus ensuring that the variable values did not change to six most significant digits. By comparing the solutions for successive grids at moderate Reynolds and Rayleigh numbers, the discretization errors were estimated to be lower than 0·1%. The results presented in this paper may thus serve for comparison purposes as bench-mark solutions.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650150306
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  • 5
    Electronic Resource
    Electronic Resource
    A collocated finite volume method for predicting flows at all speeds (1993)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 16 (1993), S. 1029-1050 
    Details
    ISSN: 0271-2091
    Keywords: Finite volume ; Compressible flow ; Subsonic flow ; Transonic flow ; Supersonic flow ; 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 existing two-dimensional method for the prediction of steady-state incompressible flows in complex geometry is extended to treat also compressible flows at all speeds. The primary variables are the Cartesian velocity components, pressure and temperature. Density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm, which in the limit of incompressible flow reduces to its well-known form. Special attention is paid to the numerical treatment of boundary conditions. The method is verified on a number of test cases (inviscid and viscous flows), and both the results and convergence properties compare favourably with other numerical results available in the literature.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650161202
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Finite volume method for prediction of fluid flow in arbitrarily shaped domains with moving boundaries (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 10 (1990), S. 771-790 
    Details
    ISSN: 0271-2091
    Keywords: Finite volume ; Conservative ; Prediction ; Fluid flow ; Moving grid ; 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: In this paper a method is presented that can be used for both the Lagrangian and the Eulerian solution of the Navier-Stokes equations in a domain of arbitrary shape, bounded by boundaries which move in any prescribed time-varying fashion. The method uses the integral form of the governing equations for an arbitrary moving control volume, with pressure and Cartesian velocity components as dependent variables. Care is taken to also satisfy the space conservation law, which ensures a fully conservative computational procedure. Fully implicit temporal differencing makes the method stable for any time step.A detailed description is provided for the discretization in two dimensions, with a collocated arrangement of variables. Central differences are used to evaluate both the convection and diffusion fluxes. The well known SIMPLE algorithm is employed for pressure-velocity coupling. The resulting algebraic equation systems are solved iteratively in a sequential manner. Results are presented for a flow in a channel with a moving indentation; they show favourable agreement with experimental observations.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650100705
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  • 7
    Electronic Resource
    Electronic Resource
    BENCHMARK SOLUTIONS OF SOME STRUCTURAL ANALYSIS PROBLEMS USING FINITE-VOLUME METHOD AND MULTIGRID ACCELERATION (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 1893-1908 
    Details
    ISSN: 0029-5981
    Keywords: finite-volume stress analysis ; multigrid ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a set of benchmark test cases for solid-body stress analysis and their solutions are presented. The results are obtained using finite-volume discretization and segregated solution procedure. Sets of progressively finer grids are used in a full multigrid algorithm based on V cycles and a correction scheme, ensuring high computational efficiency. Solutions obtained on systematically refined grids are used to estimate the solution error, which was found to be less than 1 per cent on the finest grids. In addition to graphical presentation of the solutions, tabular data for some characteristic profiles is included to make future comparisons easier. Some details about the convergence properties of the method as well as an outline of the methodology are also presented. It is hoped that the test problems and the solutions presented in this paper will be used in the future for assessing the accuracy and efficiency of new solution methods for solid-body stress analysis. © 1997 by John Wiley & Sons, Ltd.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Finite volume method for stress analysis in complex domains (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 3751-3766 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper an alternative to the widely used finite element method for the solution of stress analysis problems is presented. The method employs a finite volume discretization of solid body equilibrium equation written in an integral form with displacement vector as a dependent variable in conjunction with an efficient iterative procedure for the solution of resulting algebraic equations. It uses unstructured meshes with arbitrary cell topology, which greatly facilitates the solution domain discretization.The method is verified on a number of test cases and it is shown to possess all the geometrical flexibility of the finite element methods and the simplicity and efficiency of the finite volume methods.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620372110
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    Paper (German National Licenses)
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