Paul Labbe

Interpolation‐free space–time remeshing for the Burgers Equation

We present a mesh management strategy for use with discontinuous-Galerkin space-time finite element formulations of flow problems. We propose a refinement technique for simplex-type meshes which requires no interpolation between grids at slab interfaces. The strategy uses an a posteriori spatial error estimator to tag refinement or coarsening. Orientation of element edges along flow characteristics is accomplished by nodal displacement, and by a new diagonal-swapping technique to correct for the effects of misalignment due to h-refinement. The swapping procedure realigns the mesh to improve the effectiveness of the h-adaptive process. Results are presented for the Burgers Equation using large time steps on a problem which exhibits merging and steepening fronts

Unstructured tetrahedral mesh adaptation for two-dimensional space-time finite elements

Space-time finite elements in two dimensions require the construction of a three-dimensional mesh within each time slab. To control the accuracy of the transient solution, mesh adaptation of the time slabs usually implies the interpolation of the solution at the interface between the current and the previous time slabs. Such interpolation introduces excessive diffusion for transient solution. The approach proposed in this paper is to adapt the mesh inside the time slab, with the restriction that the twodimensional unstructured triangular mesh at the bottom of the time slab (previous time level) must be unmodified. This eliminates the interpolation of the solution and the diffusion it produces.

Solution Adaptive Refinement of Multiblock Decompositions

Conformal refinement of two and three-dimensional block decompositions for structured mesh generation is proposed using a shrink and connect operator. This operator selectively contracts and reconnects blocks according to an anisotropic metric field. The Hessian of the computed numerical flow solution is used to construct this control metric. A vertex relocation algorithm further enhances clustering in critical regions of the flow. Both two and three-dimensional examples with actual coupling to a flow solver show the feasibility of the proposed approach. Additional work is, however, needed to fine tune the adaptation process before tackling practical applications.

ANISOTROPIC HYBRID MESH ADAPTATION USING A METRIC FIELD

A formulation of an adaptive mesh method for the computation of viscous flows on hybrid meshes is presented in the paper. To control the adaptation process, the method uses a target metric field which represents the desired size, stretching and orientation of the mesh throughout the entire flow field. The metric is based on the Hessian of the Mach flow field and represents the error on the current mesh. Local transformations are used to reduce the error of the current mesh until the prescribed convergence criterion is used. The metric field does not change throughout the adaptation step. This insures a fixed target for the mesh adaptation process. The unstructured zone is refined using the anisotropic method while in the structured zone only the density of the mesh in the direction tangent to the wall is controlled by the metric field. Results regarding the application of the method and its capabilities are presented for two test cases involving the turbulent flow over airfoils at subsonic and transonic flow regimes.