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  • 1
    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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  • 2
    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
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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