Adaptive grid generation by minimizing residuals

Authors

  • Philip Roe,

    Corresponding author
    1. W.M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, University of Michigan, FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109-2140, U.S.A.
    • Department of Aerospace Engineering, University of Michigan, FXB Building, 1320 Beal Avenue, Ann Arbor, Michigan 48109-2140, U.S.A.
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  • Hiroaki Nishikawa

    1. W.M. Keck Foundation Laboratory for Computational Fluid Dynamics, Department of Aerospace Engineering, University of Michigan, FXB Building, 1320 Beal Avenue, Ann Arbor, MI 48109-2140, U.S.A.
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Abstract

We describe recent developments in the method of fluctuation splitting, in particular the minimization of residuals with respect to both the nodal values of the solution and also the nodal co-ordinates. For elliptic problems, including external (lifting) flows, obtaining good results requires that the residuals be evaluated to third order. Solutions to typical airfoil problems can then be obtained with very economical grids. For hyperbolic problems, only a second-order evaluation of the residual is needed. Shocks can be incorporated with arbitrarily high resolution by allowing elements to shrink to zero area, but to exclude the possibility of rarefaction shocks an adaptive quadrature must be employed. Copyright © 2002 John Wiley & Sons, Ltd.

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