Time Accurate Anisotropic Goal-Oriented Mesh Adaptation for Unsteady Flows

Anca Belme Alain Dervieux (INRIA, BP93, 06902 Sophia-Antipolis, France) Fréderic Alauzet (INRIA, Rocquencourt)

Article in J. Comp. Phys., 2012 (25 pages)

Abstract: We present a new algorithm for combining an anisotropic goal-oriented error estimate with the mesh adaptation fixed point method for unsteady problems. The minimization of the error on a functional provides both the density and the anisotropy (stretching) of the optimal mesh. They are expressed in terms of state and adjoint. This method is used for specifying the mesh for a time sub-interval. A global fixed point iterates the re-evaluation of meshes and states over the whole time interval until convergence of the space-time mesh. Applications to unsteady blast-wave and acoustic-wave Euler flows are presented.

Keywords: Unsteady compressible flow, goal-oriented mesh adaptation, anisotropic mesh adaptation, adjoint, metric

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@article{BDA12,
  author = {Belme, A. and Dervieux, A. and Alauzet, F.},
  title = {Time Accurate Anisotropic Goal-Oriented Mesh Adaptation for Unsteady Flows},
  journal = {J. Comp. Phys.},
  volume = {231},
  number = {19},
  pages = {6323-6348},
  year = 2012
}