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  • 1
    Electronic Resource
    Electronic Resource
    An Eulerian approach for die compaction processes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 509-524 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the analysis of deformation processes the Eulerian approach is usually formulated in material velocities. To describe the die compaction of compressible media, this paper presents an Eulerian simulation method, basically expressed in displacements. The material behaviour is modelled by the theory of elastoplasticity. Frictional interaction with the surroundings is included. As a spatially fixed finite element mesh is applied, rezoning is governed by the process specification and not, as in the Lagrangian approach, by the mesh distortion. The solution scheme, using a Newton-Raphson algorithm, is considered in detail. A consistent iteration procedure is derived. Examples demonstrate the merits of the method developed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310307
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  • 2
    Electronic Resource
    Electronic Resource
    GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS (1996)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 39 (1996), S. 3391-3403 
    Details
    ISSN: 0029-5981
    Keywords: continuum damage mechanics ; localization ; gradient dependence ; finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Conventional continuum damage descriptions of material degeneration suffer from loss of well-posedness beyond a certain level of accumulated damage. As a consequence, numerical solutions are obtained which are unacceptable from a physical point of view. The introduction of higher-order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models. A consistent numerical solution procedure of the governing partial differential equations is presented, which is shown to be capable of properly simulating localization phenomena.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Continuity conditions for finite element analysis of solids (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 845-853 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In conventional finite element formulations the concept of node - a point where one of the shape functions is unitary and all others are nil - is used to advantage as it simplifies the definition of interelement continuity conditions.This constraint on the definition of the shape functions hinders the formulation of elements with complex shapes and, in particular, of equilibrium elements.In the approach presented herein linearly independent functions are defined within each element irrespectively of the location of the nodes. Interelement continuity conditions are imposed ‘a posteriori’, as in hybrid elements.The derivation of the element matrices is based upon the equations expressing equilibrium, compatibility and the constitutive relations without explicitly using variational principles.This results in a wider choice of available funciiuns ami in an easier way to formulate equilibrium elements and/or to use conforming or non-conforming elements.As the approach used is independent of the choice of basic functions and of the shape of the elements, it is perfectly general. It allows the parallel analysis of kinematically and statically admissible formulations, as proposed by Fraeijs de Veubeke.1As the interelement continuity conditions are imposed ‘a posteriori’ new variables are used to express this condition.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620330411
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  • 4
    Electronic Resource
    Electronic Resource
    Numerical flow modelling in a locally refined grid (1994)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 497-515 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm is presented to model two-dimensional, non-isothermal, low Mach number flows with a local steep density gradient. The algorithm uses an adaptive, locally refined, non-staggered grid and has been developed, especially for modelling laminar flames. The governing equations, based on a stream-function-vorticity formulation, are presented and discretized using hybrid finite differences. A (isothermal) test problem is presented to compare the accuracy of the results of the solver presented in this paper, with the results of algorithms found in the literature. However, this test problem proves to be not well suited for the application of a locally refined grid, since it does not contain a local steep gradient. For this reason an additional test problem is constructed that clearly shows the advantages of the locally refined grid as compared to a uniform grid with respect to both the calculation time as well as the number of grid nodes needed. Furthermore, a laminar premixed flame is modelled with simple chemistry to show that the algorithm, presented in this paper, converges to a stabilized flame when an adaptive grid technique is used.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620370308
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  • 5
    Electronic Resource
    Electronic Resource
    A finite element analysis of the steady laminar entrance flow in a 90° curved tube (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 275-287 
    Details
    ISSN: 0271-2091
    Keywords: Curved pipe flow ; Entrance flow ; Finite element method ; Penalty function method ; Experimental validation ; 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: A standard Galerkin finite element penalty function method is used to approximate the solution of the three-dimensional Navier-Stokes equations for steady incompressible Newtonian entrance flow in a 90° curved tube (curvature ratio δ = 1/6) for a triple of Dean numbers (κ = 41, 122 and 204). The computational results for the intermediate Dean number (κ = 122) are compared with the results of laser-Doppler velocity measurements in an equivalent experimental model. For both the axial and secondary velocity components, fair agreement between the computational and experimental results is found.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090304
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  • 6
    Electronic Resource
    Electronic Resource
    Finite element solution of flow between eccentric cylinders with viscous dissipation (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 849-865 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-stokes ; Rotating cylinders ; Viscous dissipation ; 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: A computational study of viscous flow between two eccentrically rotating cylinders is presented in which the effect of viscous dissipation is taken into account. The space discretization is based on piecewise linear finite elements with velocity stabilization, while the method of characteristics is used for time integration. Numerical results illustrate the efficiency of the adopted approach.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110610
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  • 7
    Electronic Resource
    Electronic Resource
    A finite element approximation of the unsteady two-dimensional Navier-Stokes equations (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 427-443 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes ; Equations ; Time Integration ; Penalty Function Approach ; Oscillating Flow ; Vortex Shedding ; 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 penalty finite element solution method for the unsteady Navier-Stokes equations for two-dimensional incompressible flow is described. The performances of the Euler implicit (EI) and the Crank-Nicolson (CN) time integration methods are analysed. Special attention is payed to the undamped pressure oscillations which can occur when the Crank-Nicolson integration rule is used in combination with the penalty function method. Stability and convergence properties are illustrated by means of the computation of fully developed oscillating flow between two flat plates. Furthermore, the von Karman vortex street past a circular cylinder is computed to demonstrate the behaviour of the time integration schemes for a more complicated flow. It is concluded that the EI method has its advantages over the CN method with respect to the damping of numerical oscillations. However, for flows with an important convective contribution, where physically originated oscillations may be present, the CN method is preferable.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650060703
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  • 8
    Electronic Resource
    Electronic Resource
    AN APPROXIMATE PROJECTION SCHEME FOR INCOMPRESSIBLE FLOW USING SPECTRAL ELEMENTS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 22 (1996), S. 673-688 
    Details
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; projection methods ; operator splitting ; spectral element methods ; 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 approximate projection scheme based on the pressure correction method is proposed to solve the Navier-Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high-order spectral element method is chosen. The high-order accuracy allows the use of a diagonal mass matrix, resulting in a very efficient algorithm. The properties of the scheme are extensively tested by means of an analytical test example. The scheme is further validated by simulating the laminar flow over a backward-facing step.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Natural convection in a square cavity: A comparison exercise (1983)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 227-248 
    Details
    ISSN: 0271-2091
    Keywords: Comparison ; Natural Convection ; Numerical Methods ; Validation ; 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: A number of contributed solutions to the problem of laminar natural convection in a square cavity have been compared with what is regarded as a solution of high accuracy. The purposes of this exercise have been to confirm the accuracy of the bench mark solution and to provide a basis for the assessment of the various methods and computer codes used to obtain the contributed solutions.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650030304
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  • 10
    Electronic Resource
    Electronic Resource
    Natural convection of air in a square cavity: A bench mark numerical solution (1983)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 249-264 
    Details
    ISSN: 0271-2091
    Keywords: Natural Convection ; Numerical Methods ; Bench Mark Solution ; Square Cavity ; 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: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103≤Ra≤10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650030305
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