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  • Engineering  (13)
  • Velocity-vorticity  (2)
  • Shock wave-boundary layer interaction  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Letters to the editor (1981)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 17 (1981), S. 1740-1742 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620171112
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A finite element approach to subsonic aerodynamics (1979)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 14 (1979), S. 665-679 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A study of the application of the Finite Element Method to compressible potential flows, typified by the airfoil problem, is undertaken. Some novel approaches, believed to simplify solution techniques, are presented.The solutions use two pseudo-variational integrals, appropriate to subsonic flows, and possessing a physical iterative basis. With constant-derivatives triangular elements formulated for cylindrical co-ordinates, accurate solutions are easily obtained for the flow over a circular cylinder. For arbitrary airfoils a simple mapping is used to transform them into near circles. An appropriate mesh is then constructed in the mapped plane. The paper then presents two solution approaches by which this non-linear problem is solved in both the near circle plane and the airfoil plane.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620140504
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Conservative calculations of non-isentropic transonic flows (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 1047-1057 
    Details
    ISSN: 0271-2091
    Keywords: Transonic Flow ; Modified Potential ; Finite Elements ; Non-isentropic Flow ; Conservative Method ; 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: The classical potential formulation of inviscid transonic flows is modified to account for non-isentropic effects. The density is determined in terms of the speed as well as the pressure, which in turn is calculated from a second-order mixed-type equation derived via differentiating the momentum equations.The present model differs in general from the exact inviscid Euler equations since the flow is assumed irrotational. On the other hand, since the shocks are not isentropic, they are weaker and are placed further upstream compared to the classical potential solution. Furthermore, the streamline leaving the aerofoil does not necessarily bisect the trailing edge.Results for the present conservative calculations are presented for non-lifting and lifting aerofoils at subsonic and transonic speeds and compared to potential and Euler solutions.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650051204
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Finite element solution of the Navier-Stokes equations by a velocity-vorticity method (1990)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 11 (1990), S. 661-675 
    Details
    ISSN: 0271-2091
    Keywords: Finite elements ; Navier-Stokes ; Velocity-vorticity ; 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 velocity-vorticity formulation of the Navier-Stokes equations is presented as an alternative to the primitive variables approach. The velocity components and the vorticity are solved for in a fully coupled manner using a Newton method. No artificial viscosity is required in this formulation. The pressure is updated by a method allowing natural imposition of boundary conditions. Incompressible and subsonic results are presented for two-dimensional laminar internal flows up to high Reynolds numbers.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650110511
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Transonic viscous-inviscid interaction by a finite element method (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 309-319 
    Details
    ISSN: 0271-2091
    Keywords: Viscous-inviscid interaction ; Shock wave-boundary layer interaction ; Boundary layers ; Finite element method for flow problems ; Zonal methods ; Choked viscous flows ; Stream function-vorticity formulation ; 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 method is outlined for solving two-dimensional transonic viscous flow problems, in which the velocity vector is split into the gradient of a potential and a rotational component. The approach takes advantage of the fact that for high-Reynolds-number flows the viscous terms of the Navier-Stokes equations are important only in a thin shear layer and therefore solution of the full equations may not be needed everywhere. Most of the flow can be considered inviscid and, neglecting the entropy and vorticity effects, a potential model is a good approximation in the flow core. The rotational part of the flow can then be calculated by solution of the potential, streamfunction and vorticity transport equations. Implementation of the no-slip and no-penetration boundary conditions at the walls provides a simple mechanism for the interaction between the viscous and inviscid solutions and no extra coupling procedures are needed. Results are presented for turbulent transonic internal choked flows.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130304
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    Paper (German National Licenses)
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  • 6
    Electronic Resource
    Electronic Resource
    Finite element solution of the incompressible Navier-Stokes equations by a Helmholtz velocity decomposition (1991)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 13 (1991), S. 135-144 
    Details
    ISSN: 0271-2091
    Keywords: 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: Finite element solution methods for the incompressible Navier-Stokes equations in primitive variables form are presented. To provide the necessary coupling and enhance stability, a dissipation in the form of a pressure Laplacian is introduced into the continuity equation. The recasting of the problem in terms of pressure and an auxiliary velocity demonstrates how the error introduced by the pressure dissipation can be totally eliminated while retaining its stabilizing properties. The method can also be formally interpreted as a Helmholtz decomposition of the velocity vector.The governing equations are discretized by a Galerkin weighted residual method and, because of the modification to the continuity equation, equal interpolations for all the unknowns are permitted. Newton linearization is used and at each iteration the linear algebraic system is solved by a direct solver. Convergence of the algorithm is shown to be very rapid. Results are presented for two-dimensional flows in various geometries.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650130202
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A second order finite element method for the solution of the transonic Euler and Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 671-693 
    Details
    ISSN: 0271-2091
    Keywords: airfoil ; artificial viscosity ; upwinding ; 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: The numerical solution of the compressible Euler and Navier-Stokes equations in primitive variables form requires the use of artificial viscosity or upwinding. Methods that are first-order-accurate are too dissipative and reduce the effective Reynolds number substantially unless a very fine grid is used. A first-order finite element method for the solution of the Euler and Navier-Stokes equations can be constructed by adding Laplacians of the primitive variables to the governing equations. Second-order schemes may require a fourth-order dissipation and higher-order elements. A finite element approach is proposed in which the fourth-order dissipation is recast as the difference of two Laplacian operators, allowing the use of bilinear elements. The Laplacians of the primitive variables of the first-order scheme are thus balanced by additional terms obtained from the governing equations themselves, tensor identities or other forms of nodal averaging. To demonstrate formally the accuracy of this scheme, an exact solution is introduced which satisfies the continuity equation identically and the momentum equations through forcing functions. The solutions of several transonic and supersonic inviscid and laminar viscous test cases are also presented and compared to other available numerical data.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200802
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    A DIRECTIONALLY ADAPTIVE METHODOLOGY USING AN EDGE-BASED ERROR ESTIMATE ON QUADRILATERAL GRIDS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 673-690 
    Details
    ISSN: 0271-2091
    Keywords: Euler equations ; directionally adaptive meshes ; edge-based error estimate ; structured grids ; mesh movement ; finite element method ; high-speed flows ; 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: The present paper describes a directionally adaptive finite element method for high-speed flows, using an edge-based error estimate on quadrilateral grids. The error of the numerical solution is estimated through its second derivatives and the resulting Hessian tensor is used to define a Riemannian metric. An improved mesh movement strategy, based on a spring analogy, but with no orthogonality constraints, is introduced to equidistribute the lengths of the edges of the elements in the defined metric. The grid adaptation procedure is validated on an analytical test case and the efficiency of the overall methodology is investigated on supersonic and hypersonic benchmarks.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Numerical solution of subsonic and transonic cascade flows (1982)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 2 (1982), S. 317-330 
    Details
    ISSN: 0271-2091
    Keywords: Transonic flow ; Turbomachines ; Finite elements ; 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 work a study of the application of the finite element method to transonic flows in axial turbomachines is undertaken.Solution techniques capable of accurately predicting flows from the incompressible regime up to the establishment of shocks in the transonic regime are presented. In the subsonic and shockless transonic regimes a local linearization method capable of very rapid convergence is used. In the full transonic regime the artificial compressibility method is employed to exclude downstream influences in the supersonic regions. The two approaches can be combined in a unified package and appropriate switches introduced to select the relevant method in any flow regime.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650020402
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  • 10
    Electronic Resource
    Electronic Resource
    A transonic quasi-3D analysis for gas turbine engines including split-flow capability for turbofans (1983)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 3 (1983), S. 1-21 
    Details
    ISSN: 0271-2091
    Keywords: Turbomachines ; Finite Elements ; Transonic Flows ; 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 numerical approximation is taken to the solution of the complex flows existing in gas turbine engines with transonic blading. The quasi-3D approach decouples the problem into through-flow and blade-to-blade solutions. An industrially practical finite element through-flow solution is developed and for blade-to-blade solutions a transonic finite areas method is utilized. The finite element code developed is capable of operating in an analysis or a design mode. In both modes a dynamic relaxation factor is employed and considerable reduction in solution time can be achieved. Comparisons to streamline curvature methods are carried out for simple analytical and complex industrial problems.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650030103
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    Paper (German National Licenses)
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