Julien Dompierre

Anisotropic mesh adaptation: towards user‐independent, mesh‐independent and solver‐independent CFD. Part I: general principles

The present paper is the lead article in a three-part series on anisotropic mesh adaptation and its applications to structured and unstructured meshes. A flexible approach is proposed and tested on two-dimensional, inviscid and viscous, finite volume and finite element flow solvers, over a wide range of speeds. The directional properties of an interpolation-based error estimate, extracted from the Hessian of the solution, are used to control the size and orientation of mesh edges. The approach is encapsulated into an edge-based anisotropic mesh optimization methodology (MOM), which uses a judicious sequence of four local operations: refinement, coarsening, edge swapping and point movement, to equi-distribute the error estimate along all edges, without any recourse to remeshing. The mesh adaptation convergence of the MOM loop is carefully studied for a wide variety of test cases

A finite element method study of Eulerian droplets impingement models

To compute droplet impingement on airfoils, an Eulerian model for air flows containing water droplets is proposed as an alternative to the traditional Lagrangian particle tracking approach. Appropriate boundary conditions are presented for the droplets equations, with a stability analysis of the solution near the airfoil surface. Several finite element formulations are proposed to solve the droplets equations, based on conservative and non-conservative forms and using different stabilization terms. Numerical results on single and multi-elements airfoils for droplets of mean volume diameter, as well as for a Langmuir distribution of diameters, are presented and validated against measured values

Certifiable Computational Fluid Dynamics Through Mesh Optimization

The accuracy and reliability of computational fluid dynamics (CFD) are addressed by proposing a novel, efficient, and generic mesh optimization approach. By using an appropriate directional error estimator, coupled with an effective mesh adaptation technique that is tied closely to the solver, it can be demonstrated that, for each flow condition and geometry combination, a controllable error level and an optimal mesh can be obtained. It is further demonstrated that such an optimal mesh can be reached from almost any reasonable initial grid and, more astonishingly, that the order of accuracy of well-posed numerical algorithms has a considerably reduced impact on solution accuracy if the mesh is well adapted. Thus, the proposed approach can be considered a first step toward user-, mesh-, and solver-independent, and thus certifiable, CFD.

Two-dimensional metric tensor visualization using pseudo-meshes

Riemannian metric tensors are used to control the adaptation of meshes for finite element and finite volume computations. To study the numerous metric construction and manipulation techniques, a new method has been developed to visualize two-dimensional metrics without interference from an adaptation algorithm. This method traces a network of orthogonal tensor lines, tangent to the eigenvectors of the metric field, to form a pseudo-mesh visually close to a perfectly adapted mesh but without many of its constraints. Anisotropic metrics can be visualized directly using such pseudo-meshes but, for isotropic metrics, the eigensystem is degenerate and an anisotropic perturbation has to be used. This perturbation merely preserves directional information usually present during metric construction and is small enough, about 1% of the prescribed target element size, to be visually imperceptible. Both analytical and solution-based examples show the effectiveness and usefulness of the present method. As an example, pseudo-meshes are used to visualize the effect on metrics of Laplacian-like smoothing and gradation control techniques. Application to adaptive quadrilateral mesh generation is also discussed.

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.

Adaptive mesh generation of MRI images for 3D reconstruction of human trunk

This paper presents an adaptive mesh generation method from a series of transversal MR images. The adaptation process is based on the construction of a metric from the gray levels of an image. The metric is constrained by four parameters which are the minimum and maximum Euclidian length of an edge, the maximum stretching of the metric and the target edge length in the metric. The initial mesh is a regular triangulation of an MR image. This initial mesh is adapted according to the metric by choosing appropriate values for the previous set of parameters. The proposed approach provides an anisotropic mesh for which the elements are clustered near the boundaries. The experimental results show that the elements edges of the obtained mesh are aligned with the boundaries of anatomical structures identified on the MR images. Furthermore, this mesh has approximately 80% less vertices than the mesh before adaptation with vertices mainly located in the regions of interest.

3D casing-distributor analysis with a novel block coupled OpenFOAM solver for hydraulic design application

Nowadays, computational fluid dynamics is commonly used by design engineers to evaluate and compare losses in hydraulic components as it is less expensive and less time consuming than model tests. For that purpose, an automatic tool for casing and distributor analysis will be presented in this paper. An in-house mesh generator and a Reynolds Averaged Navier-Stokes equation solver using the standard k-ω SST turbulence model will be used to perform all computations. Two solvers based on the C++ OpenFOAM library will be used and compared to a commercial solver. The performance of the new fully coupled block solver developed by the University of Lucerne and Andritz will be compared to the standard 1.6ext segregated simpleFoam solver and to a commercial solver. In this study, relative comparisons of different geometries of casing and distributor will be performed. The present study is thus aimed at validating the block solver and the tool chain and providing design engineers with a faster and more reliable analysis tool that can be integrated into their design process.

Applying Parmetis to Structured Remeshing for Industrial CFD Applications

This paper presents the current strategy used in IP-OORT, an ongoing project to extend the application domain of a C++ toolkit library for iterative mesh adaptation. OORT is a class library for sequential structured, unstructured and hybrid mesh adaptation used mainly in the context of CFD computations, that performs iterative mesh refinement, coarsening and smoothing in 3D. Extensions to parallelize mesh adaptation using ParMeTiS for domain decomposition and MPI high-level communication schemes are investigated here. Numerical simulations on realistic cases show that the parallel strategy scales with problem size and the number of processors, but singular behaviors are sometimes encountered at subdomain interfaces when conflicting instructions collide.

On ellipse intersection and union with application to anisotropic mesh adaptation

This paper presents ellipses as a convenient mean of representation for operating on several tensor fields. The first part of this paper discusses the representation of tensors as ellipses or ellipsoids. Two binary operators are defined inside the set of centred ellipses, intersection, and union, and their properties are studied. The second part of this paper presents an application of these operators to binary operations on metric tensor fields for the purpose of anisotropic mesh adaptation.

Mesh convergence study for hydraulic turbine draft-tube

Computational flow analysis is an essential tool for hydraulic turbine designers. Grid generation is the first step in the flow analysis process. Grid quality and solution accuracy are strongly linked. Even though many studies have addressed the issue of mesh independence, there is still no definitive consensus on mesh best practices, and research on that topic is still needed. This paper presents a mesh convergence study for turbulence flow in hydraulic turbine draft- tubes which represents the most challenging turbine component for CFD predictions. The findings from this parametric study will be incorporated as mesh control rules in an in-house automatic mesh generator for turbine components.