h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems

In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh sequences are generated by recursive agglomeration of a fine grid, admitting arbitrarily unstructured grids of complex domains, and agglomeration based discontinuous Galerkin discretizations are employed to deal with agglomerated elements of coarse levels. Both the expense of building coarse grid operators and the performance of the resulting multigrid iteration are investigated. For the sake of efficiency coarse grid operators are inherited through element-by-element $L^2$ projections, avoiding the cost of numerical integration over agglomerated elements. Specific care is devoted to the projection of viscous terms discretized by means of the BR2 dG method. We demonstrate that enforcing the correct amount of stabilization on coarse grids levels is mandatory for achieving uniform convergence with respect to the number of levels. The numerical solution of steady and unsteady, linear and non-linear problems is considered tackling challenging 2D test cases and 3D real life computations on parallel architectures. Significant execution time gains are documented.Comment: 78 pages, 7 figure

HexBox: Interactive Box Modeling of Hexahedral Meshes

We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box-model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non-conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally-provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid- based meshing, such as mixing of 3-refinement, 2-refinement, and face-refinement, and using templated topological bridges to enforce on-the-fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques

Guidelines to select suitable parameters for contour method stress measurements

The contour method is one of the promising techniques for the measurement of residual stresses in engineering components. In this method, the cut surfaces deform, owing to the relaxation of residual stresses. The deformations of the two cut surfaces are then measured and used to back calculate the 2-dimensional map of original residual stresses normal to the plane of the cut. Thus, it involves four main steps; specimen cutting, surface contour measurement, data analysis and finite element simulation. These steps should perform in a manner that they do not change the underlying features of surface deformation especially where the residual stress distribution varies over short distances. Therefore, to carefully implement these steps, it is important to select appropriate parameters such as surface deformation measurement spacing, data smoothing parameters (‘knot spacing’ for example cubic spline smoothing) and finite element mesh size. This research covers an investigation of these important parameters. A simple approach for choosing initial parameters is developed based on an idealised cosine displacement function (giving a self-equilibrated one-dimensional residual stress profile). In this research, guidelines are proposed to help the measurer to select the most suitable choice of these parameters based on the estimated wavelength of the residual stress field

On curving high-order hexahedral meshes

We present a new definition of distortion and quality measures for high-order hexahedral (quadrilateral) elements. This definition leads to two direct applications. First, it can be used to check the validity and quality of a high-order hexahedral (quadrilateral) mesh. Second, it allows the generation of high-order curved meshes composed of valid and high-quality hexahedral (quadrilateral) elements. We describe a method to simultaneously smooth and untangle high-order hexahedral (quadrilateral) meshes by minimizing the proposed mesh distortion. Finally, we analyze the behavior of the proposed distortion measure and we present several results to illustrate the benefits of the mesh generation framework.Peer ReviewedPostprint (author's final draft