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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids 2000; 00:16 Prepared using fldauth.cls [Version: 2002/09/18 v1.01]
 

Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
Int. J. Numer. Meth. Fluids 2000; 00:1­6 Prepared using fldauth.cls [Version: 2002/09/18 v1.01]
High-order methods and mesh adaptation for Euler equations
F. Alauzet
INRIA - Gamma Project, Domaine de Voluceau, Le Chesnay, 78153, France
SUMMARY
In this paper, we point out a novel contribution of mesh adaptation to high-order methods for stationary and time-
dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint-free method,
achieves a global second-order mesh convergence for numerical solutions with discontinuities in Lp norm. To
attain this result, it is mandatory to combine together all mesh adaptive methods developed in previous work. This
theoretical result is validated on 2D and 3D examples for stationary and time-dependent simulations. Copyright
c 2000 John Wiley & Sons, Ltd.
KEY WORDS: Anisotropic mesh adaptation, unstructured meshes, high-order method, Euler equations
1. INTRODUCTION
Classical high-order shock capturing methods, such as MUSCL, ENO, residual distribution scheme, ...,
are theoretically converging at order two or more. Such methods are suitable to compute discontinuous
flows which often occur for supersonic flows, blast waves, interfaces' problems, ... Nevertheless, this
theoretical order is never obtained in practice. Only an order less than one is attained when the mesh is
uniformly refined. Indeed, by meshing uniformly a segment, we can demonstrate that in a discontinuity
the interpolation error converges in O(h1/p) for Lp

  

Source: Alauzet, Frédéric - INRIA Paris-Rocquencourt

 

Collections: Computer Technologies and Information Sciences