Inverse Distance Weighting interpolation for moving mesh adaptation

  • Lissoni, G. ( SC-Consultants)
  • Hachem, E. ( Computing and Fluids Research Group)
  • Larcher, A. (Computing and Fluids Research Group)

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The aim of this paper is to present a moving mesh method in the context of dynamic fluid-structure interaction simulations which combines an explicit r-adaptation method based on Inverse Distance Weighting (IDW) with a selective h-adaptation procedure. Inverse Distance Weighting is as an interpolation method and it was first introduced by Shepard in [3]: a function is interpolated at a given point with a weighted average of the values available at the known data points; the method was then adapted to the context of mesh deformation by Witteveen in [4, 2, 1]. Given a boundary displacement vector [d1,...dN], it computes the displacement field d(x) of a point x in the rest of the volume mesh by IDW: d(x) = N ∑ n=1 wn(x)dn N ∑ n=1 wn(x) , (1) where [w1,...wN] denote some weights. The weighting function is a decreasing function of distance; this means in particular that the displacement of a point in the volume mesh is inversely proportional to the distance from the zero isovalue of the level set. Namely, this is what allows the method not to deform excessively the elements that are far from the object, since the potential action has to be negligible. We propose an hybrid method, which couples the Inverse Distance Weighting method with an efficient hadaptation process: we move the mesh nodes with IDW and, if the mesh quality deteriorates, we perform an h-adaptation only on some selected areas in order to improve locally the bad-shaped elements that are deformed by the movement. As a previous work in this direction, we refer to [1]. Our global algorithm includes: the application of an immersion technique based on the representation of geometries through Level Set method; the anisotropic mesh adaptation to the object interface and its environement; the implementation of a moving mesh strategy which guarantees a good quality along the simulation with an interesting computational cost.