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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Numerische Mathematik 81 (1999), S. 497-520 
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):76D99; 76S05
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract. From the Navier-Stokes/Brinkman model, a penalization method has been derived by several authors to compute incompressible Navier-Stokes equations around obstacles. In this paper, convergence theorems and error estimates are derived for two kinds of penalization. The first one corresponds to $L^2$ penalization inducing a Darcy equation in the solid body, the second one corresponds to a $H^1$ penalization and induces a Brinkman equation in the body. Numerical tests are performed to confirm the efficiency and accuracy of the method.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9109
    Keywords: nonlinear convection-diffusion problem ; barycentric finite volumes ; Crouzeix-Raviart nonconforming piecewise linear finite elements ; monotone finite volume scheme ; discrete maximum principle ; a priori estimates ; convergence of the method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We present the convergence analysis of an efficient numerical method for the solution of an initial-boundary value problem for a scalar nonlinear conservation law equation with a diffusion term. Nonlinear convective terms are approximated with the aid of a monotone finite volume scheme considered over the finite volume barycentric mesh, whereas the diffusion term is discretized by piecewise linear nonconforming triangular finite elements. Under the assumption that the triangulations are of weakly acute type, with the aid of the discrete maximum principle, a priori estimates and some compactness arguments based on the use of the Fourier transform with respect to time, the convergence of the approximate solutions to the exact solution is proved, provided the mesh size tends to zero.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 1163-1195 
    ISSN: 0271-2091
    Keywords: ocean circulation model ; primitive equations ; interactive nested grid model ; multidomain methods ; multigrid local mesh refinement ; local grid correction ; 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 comparison is carried out between three correction methods for multigrid local mesh refinement in oceanic applications: FIC, LDC and the direct method (DM) proposed by Spall and Holland. This study is based on a nested primitive equation model developed by Laugier on the basis of the code OPA (LODYC). The external barotropic problem is solved using any of the three local grid correction algorithms yielding an interactive nested grid model. The non-linear elliptic equation for the barotropic streamfunction tendency is solved on two nested grids, called the global and the zoom grid, that interact between themselves. The zoom grid is entirely embedded within the global domain with a horizontal grid step ratio of 3:1. The computation on the global grid supplies the boundary conditions for the zoom grid region and the fine grid fields are used to correct the global coarse solution. The three local correction methods are tested on two problems relevant to oceanic circulation phenomena proposed by Spall and Holland: a barotropic modon and an anticyclonic vortex. The results show that the nesting technique is a very efficient way to solve these problems in terms of a gain in precision compared with the required CPU time. The two-domain model with local mesh refinement allows one both to manage effectively the open boundary conditions for the local grid and to correct the global solution thanks to the zoom solution. In the case of the modon propagation the three local correction methods provide approximately the same results. For the baroclinic vortex it appears that the two iterative methods are more efficient than the direct one.
    Additional Material: 23 Ill.
    Type of Medium: Electronic Resource
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