Romain Aubry

THE PARTICLE FINITE ELEMENT METHOD — AN OVERVIEW

We present a general formulation for the analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.

Deflated preconditioned conjugate gradient solvers for the Pressure-Poisson equation

A deflated preconditioned conjugate gradient technique has been developed for the solution of the Pressure-Poisson equation within an incompressible flow solver. The deflation is done using a region-based decomposition of the unknowns, making it extremely simple to implement. The procedure has shown a considerable reduction in the number of iterations. For grids with large graph-depth the savings exceed an order of magnitude. Furthermore, the technique has shown a remarkable insensitivity to the number of groups/regions chosen, and to the way the groups are formed.

Linear Sources for Mesh Generation

Sources offer a convenient way to prescribe a size distribution in space. For each newly created mesh point, the mesh generator queries the local size distribution, either to create a new point or element, depending on the underlying mesh generation method, to smooth the mesh, or to get a local relevant length scale. Sources may have different shapes such as points, edges, triangles, or boxes. They provide the size distribution given some user defined parameters and the distance of a point location to the source. Traditionally, the source strength is considered as constant. In this work, extensions to linear sources in space are proposed. It is shown that in the case of curvature refined mesh generation, substantial savings may occur due to the much better approximation of the curvature variation for a simple modification of traditional sources. Even though curvature refinement is the main application of this work, improvements through linear sources are relevant to other contexts such as user defined sou...

A three-dimensional parametric mesher with surface boundary-layer capability

Abstract A novel parametric surface meshing technique is presented. Its distinctive feature relies on successive approximations of the CAD geometry through a hierarchical process where geometric information is gathered incrementally. A detailed review of zero- and first-order surface approximations and their impact on parametric surface meshing algorithms is performed. The proposed approach emphasizes the use of three-dimensional information in order to be as independent as possible of the parametrization to overcome limitations of meshing purely in the parametric plane. The presented technique includes semi-structured boundary-layer surface mesh generation which is a critical capability for accurate solutions to flows around geometries that have leading edge features. Numerous examples illustrate the methods robustness and ability to high-quality meshes for complex CAD geometries.

Generation of viscous grids with ridges and corners

An extension of Lohner 1 for the generation of high aspect ratio volume grids on surfaces with ridges and corners is presented for Reynolds-Averaged Navier-Stokes computations (RANS). Multiple normals are introduced along convex ridges. The original technique generates a semi-structured boundary layer of prismatic elements growing along point nor- mals. Therefore, extra faces of null area must be introduced to take into account the multiple growth curves at convex ridges and produce a valid topological surface triangu- lation. The procedure relies on a topological taxonomy of an arbitrary combination of concave and convex ridges. Each case is highlighted in details. Several complex geometries have been chosen to illustrate the proposed procedure and timings are given, showing that the new module does not place any extra burden in the previous semi-structured approach.

Capstone: A Geometry-Centric Platform to Enable Physics-Based Simulation and System Design

Capstone is a geometry-centric platform for a unified representation of the geometry, mesh, and attribution needed for engineering analyses with varying fidelity. Meshes and attributes are both associated with a robust mathematical model of the geometry, enabling any change to be automatically propagated to the meshes and attributes needed for analyses. Captsone provides a software platform with well-abstracted and compact interfaces to create, modify, and query geometry, mesh, and attribution information for a model. This forms a foundation for geometry-based design environments and solvers that can access the geometry at runtime for scalable and accurate a posteriori mesh adaptation. Capstone provides a graphical front end for computational fluid dynamics. Capstone is being used and evaluated by several US Department of Defense organizations.

A three dimensional parametric mesher

A parametric meshing technique is presented. Its distinctive feature relies on approximating the CAD geometry through a hierarchical process where information is gradually gathered. It leads to a robust and high quality mesh for CAD geometries. Emphasis is put on the use of three dimensional information. Limitations of parametric plane meshing is also highlighted. Zero and first order surface approximations are commented, and parametric mesh generation techniques are compared. In the context of the DOD CREATE-MG project, different CAD kernels and meshers communicate through application programming interfaces (API) as plugins. The parametric mesher is coupled to the CAD through the Capstone API’s and is independent of a particular CAD kernel. Numerous examples illustrate the method ’s capabilities.

Smooth anisotropic sources with application to three-dimensional surface mesh generation

Isotropic sources are extended to take anisotropy into account in order to obtain a smooth anisotropic sizing field for anisotropic mesh generation. Different types of anisotropic sources are described to represent boundary layers on surfaces and in volume that guarantee a smooth anisotropic field. This allows to us resolve multiple boundary layer intersections properly and naturally provides a smooth transition between the anisotropic boundary layer sizing and the isotropic region. Furthermore, the interaction between a smooth anisotropic sizing field and curvature is studied, and estimates of the tangential size spacing are provided for first and second order approximation of the geometry to ensure smoothness of the sizing field. It is also shown that, in order to get a smooth size variation, volumetric and surface meshing can not be decoupled. The filtering of the sources in order to obtain a computationally efficient method is described. Numerical examples demonstrate our method.

An Entropy Satisfying Boundary Layer Surface Mesh Generation

A method is presented to generate surface boundary layers. The novelty of the method consists in a uniform treatment of the concave and convex regions based on offsetting the initial front. In particular, concave situations are enforced to respect the entropy satisfying solution. Local solutions of the offset of edges in the planes and triangles in the three dimensional space are also given, showing the relationship between normal computation, distance extrusion, and the generalized Voronoi diagram. The boundary layer mesh generation is cast as a weak solution of the Eikonal equation computed locally, layer by layer, to mimic the hyperbolic character of the Eikonal equation, augmented by a possibly nonbijective mapping between layers. This provides a theoretical framework to rely on for practical answers such as configurations where the adjacent topologies to a boundary layer may be curved, or at least not aligned with the offset direction, or if the boundary layer mesh must be generated as a mapping betw...

Singularities in Parametric Meshing

A parametric meshing technique is presented with special emphasis to singularities in the parametric mapping. Singularities are locations where the parametric mapping is highly distorted or even singular. In a NURBS context, this arises when control points are clustered into the same location in three dimensions. Limitations of parametric plane meshing in this context are highlighted, and zero- and first-order surface approximations are commented. In the context of the DOD CREATE-MG project, different CAD kernels and mesh generators communicate as plugins through application programming interfaces (API). The parametric mesh generator is coupled to the CAD through the Capstone APIs and is independent of a particular CAD kernel. Some CAD kernels do not allow these geometrical constructions while some tolerate it. It is therefore a necessity to handle these degenerate cases properly. Examples illustrate the method’s capabilities.