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  • 1
    Electronic Resource
    Electronic Resource
    An asymptotic expansion for product integration applied to Cauchy principal value integrals (1975)
    Springer
    Numerische Mathematik 24 (1975), S. 435-442 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Product integration methods for Cauchy principal value integrals based on piecewise Lagrangian interpolation are studied. It is shown that for this class of quadrature methods the truncation error has an asymptotic expansion in integer powers of the step-size, and that a method with an asymptotic expansion in even powers of the step-size does not exist. The relative merits of a quadrature method which employs values of both the integrand and its first derivative and for which the truncation error has an asymptotic expansion in even powers of the step-size are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01437410
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  • 2
    Electronic Resource
    Electronic Resource
    Vertex-centered and cell-centered multigrid for interface problems
    Amsterdam : Elsevier
    Journal of Computational Physics 98 (1992), S. 1-10 
    Details
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0021-9991(92)90168-X
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  • 3
    Electronic Resource
    Electronic Resource
    Cell-centered multigrid for interface problems
    Amsterdam : Elsevier
    Journal of Computational Physics 79 (1988), S. 85-91 
    Details
    ISSN: 0021-9991
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Computer Science , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1016/0021-9991(88)90005-8
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  • 4
    Electronic Resource
    Electronic Resource
    Discretization of the Navier–Stokes equations on non-smooth grids using auxiliary points (1999)
    Springer
    Computing and visualization in science 2 (1999), S. 69-73 
    Details
    ISSN: 1433-0369
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. The colocated scheme for the incompressible Navier–Stokes equations is improved on structured non-Cartesian grids. The method relies on a finite volume discretization and on the use of auxiliary points to locally approximate gradients following a two-point discretization. Enhanced accuracy is demonstrated for two-dimensional cases on strongly distorted meshes by computing Poiseuille flow and a flow in a differentially heated cavity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007910050029
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  • 5
    Electronic Resource
    Electronic Resource
    A staggered scheme for hyperbolic conservation laws applied to unsteady sheet cavitation (1999)
    Springer
    Computing and visualization in science 2 (1999), S. 63-68 
    Details
    ISSN: 1433-0369
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. We demonstrate the advantages of discretizing on a staggered grid for the computation of solutions to hyperbolic systems of conservation laws arising from instationary flow of an inviscid fluid with an arbitrary equation of state. Results for a highly nonlinear, nonconvex equation of state obtained with the staggered discretisation are compared with those obtained with the Osher scheme for two different Riemann problems. The staggered approach is shown to be superior in simplicity and efficiency, without loss of accuracy. The method has been applied to simulate unsteady sheet cavitation on a NACA0012 hydrofoil. Results show good agreement with those obtained with a cavity interface tracking method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s007910050028
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  • 6
    Electronic Resource
    Electronic Resource
    The ISNaS incompressible Navier-Stokes solver: invariant discretization (1994)
    Springer
    Flow, turbulence and combustion 48 (1994), S. 175-191 
    Details
    ISSN: 1573-1987
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The ISNaS-project aims at providing tools for computer aided design and engineering in aerodynamics and hydrodynamics by developing an Information System for the simulation of complex flows based on the Navier-Stokes equations. Major components of the project are the development of a method-shell and of accurate as well as robust solvers for both compressible and incompressible flows. For the incompressible case, guided by typical applications in the field of river and coastal hydrodynamics, a solution procedure is being developed that is capable of handling complicated geometries, including free surface effects, in particular for high-Reynolds number flow regimes. In the present paper the invariant discretization of the incompressible Navier-Stokes equations in general boundary-fitted coordinate systems is discussed. It is found to be important that certain rules are followed concerning the choice of unknowns and the approximation of the geometric quantities. This is illustrated by some preliminary results. Extensions to moving coordinate systems and time-varying computational grids are indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02027966
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  • 7
    Electronic Resource
    Electronic Resource
    On the construction of accurate difference schemes for hyperbolic partial differential equations (1973)
    Springer
    Journal of engineering mathematics 7 (1973), S. 19-31 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary Methods are developed for increasing the fidelity of difference approximations to hyperbolic partial differential equations. A relation between the truncation error and the exact and approximate amplification factors is derived. Based upon this relation, quantitative criteria for the minimization of dissipation and dispersion are derived, and difference schemes which satisfy these criteria are constructed. Completely new schemes, one of them promising, are obtained, together with several well-known schemes. One of these is the Fromm scheme, for which previously only a heuristic derivation could be given. It is shown that in general the accuracy of the Rusanov-Burstein-Mirin scheme is disappointing. A simple modification was found to remedy this deficiency.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01535266
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical solution of the incompressible Navier-Stokes equations by Krylov subspace and multigrid methods (1995)
    Springer
    Advances in computational mathematics 4 (1995), S. 27-49 
    Details
    ISSN: 1572-9044
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider numerical solution methods for the incompressible Navier-Stokes equations discretized by a finite volume method on staggered grids in general coordinates. We use Krylov subspace and multigrid methods as well as their combinations. Numerical experiments are carried out on a scalar and a vector computer. Robustness and efficiency of these methods are studied. It appears that good methods result from suitable combinations of GCR and multigrid methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02123472
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  • 9
    Electronic Resource
    Electronic Resource
    Local Grid Refinement in Large-Eddy Simulation (1997)
    Springer
    Journal of engineering mathematics 32 (1997), S. 161-175 
    Details
    ISSN: 1573-2703
    Keywords: large-eddy simulations ; local grid refinement ; turbulence.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract A method for performing nested-grid calculations with a Large-Eddy Simulation (LES) code is described. The grid consists of a coarse mesh and a fine mesh which overlaps the coarse in some region. A standard finite-volume method is used on both meshes. By means of grid communication, the velocity and pressure at both meshes are matched. To check that large eddies which are already resolved on the coarse grid are not affected by the nesting procedure, a simple two-dimensional mixing layer is simulated. Several simulations of this flow have been carried out with a different number of grid points on the nested grid. It is found that, without much extra computational effort, the grid-nesting improves the turbulent statistics with respect to the results found on the coarse mesh. This improvement occurs first of all in the region where grid refinement is applied, but better results are also found on the coarse mesh outside the grid-refinement region. Furthermore, it is shown that the large-scale structures in this flow are not influenced by the boundary between the coarse and fine grid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004283921077
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  • 10
    Electronic Resource
    Electronic Resource
    Computing Flow on General Two-Dimensional Nonsmooth Staggered Grids (1998)
    Springer
    Journal of engineering mathematics 34 (1998), S. 21-44 
    Details
    ISSN: 1573-2703
    Keywords: Navier-Stokes ; finite volume discretization ; staggered grids ; boundary-fitted coordinates.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract The classical staggered scheme for the incompressible Navier-Stokes equations is generalized from Cartesian grids to general boundary-fitted structured grids. The resulting discretization is coordinate-invariant. The unknowns are the pressure and the contravariant volume flux components. The grid can be strongly nonuniform and nonorthogonal. The smoothness properties of the coordinate mapping are carefully taken into account. As a result, the accuracy on rough grids is found to be at least as good as for typical finite element and nonstaggered finite volume schemes. Extension to compressible flows results in a scheme with Mach-uniform accuracy and efficiency for Mach numbers ranging from M = 0 to M 〉 1. Accurate discretization of two-equation turbulence models is also possible.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004341115180
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