A feature-based mesh adaptation for the unsteady high speed compressible flows in complex three-dimensional domains

We propose an unstructured mesh adaptation approach for unsteady high speed compressible Navier–Stokes applications involving blasts and explosions with the presence of strong shock waves propagating in three dimensional complex domains. The idea is to identify the locations of critical physics locally and then re-mesh these regions based on solution derived metrics. The approach ensures both geometry fidelity and mesh validity, especially for areas near complex geometries, a task that is always a challenge in mesh adaptation. The proposed adaptivity is applied for simulations of blast wave propagations and compared with available data in literature. The results show that the proposed method is fully robust and efficient for computational fluid dynamics (CFD) problems in complex three-dimensional domains

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd

The role of mesh generation, adaptation, and refinement on the computation of flows featuring strong shocks

Within a continuum framework, flows featuring shock waves can be modelled by means of either shock capturing or shock fitting. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms on structured grids allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. We show how recent advances in computational mesh generation allow to relieve some of the difficulties encountered by shock capturing and contribute towards making shock fitting on unstructured meshes a versatile technique

Unstructured Mesh Generation and Adaptation

International audienceWe first describe the well established unstructured mesh generation methods as involved in the computational pipeline, from geometry definition to surface and volume mesh generation. These components are always a preliminary and required step to any numerical computations. From an historical point of view, the generation of fully unstructured mesh generation in 3D has been a real challenge so as to the design of robust and accurate second order schemes on such unstructured meshes. If the issue of generating volume meshes for geometries of any complexity is now mostly solved, the emergence of robust numerical schemes on unstructured meshes has paved the way to adaptivity. Indeed, unstructured meshes in contrast with structured or block structured grids have the necessary flexibility to control the discretization both in size and orientation. In the second part, we review the main components to perform adaptative computations: (i) anisotropic mesh prescription via a metric field tensor (ii) anisotropic error estimates, and (iii) anisotropic mesh generation. For each component, we focus on a particularly simple method to implement. In particular, we describe a simple but robust strategy for generating anisotropic meshes. Each adaptation entity, ie surface, volume or boundary layers, relies on a specific metric tensor field. The metric-based surface estimate is then used to control the deviation to the surface and to adapt the surface mesh. The volume estimate aims at controlling the interpolation error of a specific field of the flow. Several 3D examples issued from steady and unsteady simulations from systems of hyper-bolic laws are presented. In particular, we show that despite the simplicity of the introduced adaptive meshing scheme a high level of anisotropy can be reached. This includes the direct prediction of the sonic boom of an aircraft by computing the flow from the cruise altitude to the ground, the interaction between shock waves and boundary layer, or the prediction of complex unsteady phenomena in 3D

Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

Anisotropic Adaptation on Unstructured Grids

The efficient representation of the highly directional features in a flow field with adapted anisotropic grids forms the focus of the analysis. Anisotropic adaptation is more effective than isotropic adaptation and requires more degrees of freedom from the mesh, which also demands the use of unstructured grids in the adaptation. The size and orientation of an anisotropic element require a matrix-like local feature indicator. The Hessian, a matrix composed of the second derivatives of an appropriate flow variable, is defined and used as a feature indicator in the adaptation. The Hessian provides a metric that defines the length of an edge and the lengths of all edges are equal in the optimized mesh. The techniques to minimize the differences among edge lengths are discussed and those chosen include node enrichment, node removal, edge swapping and point smoothing. The results indicate that the mesh in which the edge lengths are equalized is not correct for three major flow features one frequently encounters. The inflections existing near the wall in a boundary layer result in coarse grids there. A “wall” Hessian is defined to replace the second derivatives and give a more appropriate spacing for high Reynolds number flow modeling. Difficulties in the adaptation of discontinuities are addressed. Remedies proposed are to limit the minimum physical edge length and smooth the Hessian such that the discontinuity refinement encompasses more layers of elements. The methodology to refine the discontinuity equally is also proposed. The invalidity of the Hessian in a free stream is corrected to give a reasonable grid size in that region. The concepts involved in the extension of the length-based approach to three dimensions are addressed. The difference and difficulties in three-dimensional adaptation are discussed

Galerkin projection of discrete fields via supermesh construction

Interpolation of discrete FIelds arises frequently in computational physics. This thesis focuses on the novel implementation and analysis of Galerkin projection, an interpolation technique with three principal advantages over its competitors: it is optimally accurate in the L2 norm, it is conservative, and it is well-defined in the case of spaces of discontinuous functions. While these desirable properties have been known for some time, the implementation of Galerkin projection is challenging; this thesis reports the first successful general implementation. A thorough review of the history, development and current frontiers of adaptive remeshing is given. Adaptive remeshing is the primary motivation for the development of Galerkin projection, as its use necessitates the interpolation of discrete fields. The Galerkin projection is discussed and the geometric concept necessary for its implementation, the supermesh, is introduced. The efficient local construction of the supermesh of two meshes by the intersection of the elements of the input meshes is then described. Next, the element-element association problem of identifying which elements from the input meshes intersect is analysed. With efficient algorithms for its construction in hand, applications of supermeshing other than Galerkin projections are discussed, focusing on the computation of diagnostics of simulations which employ adaptive remeshing. Examples demonstrating the effectiveness and efficiency of the presented algorithms are given throughout. The thesis closes with some conclusions and possibilities for future work

A curvature-adapted anisotropic surface remeshing method

We present a new method for remeshing surfaces that respect the intrinsic anisotropy of the surfaces. In particular, we use the normal informations of the surfaces, and embed the surfaces into a higher dimensional space (here we use 6d). This allow us to form an isotropic mesh optimization problem in this embedded space. Starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by combining common local modifications operations, i.e., edge flip, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the 3d surface mesh. This method results a curvature-adapted mesh of the surface. This method can be easily adapted to mesh multi-patches surfaces, i.e., containing corner singularities and sharp features. We present examples of remeshed surfaces from implicit functions and CAD models

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

This document presents an interpolation operator on unstructured tetrahedral meshes that satisfies the properties of mass conservation, P1-exactness (order 2) and maximum principle. Interpolation operators are important for many applications in scientific computing. For instance, in the context of anisotropic mesh adaptation for time-dependent problems, the interpolation stage becomes crucial as the error due to solution transfer accumulates throughout the simulation. This error can eventually spoil the overall solution accuracy. When dealing with conservation laws in CFD, solution accuracy requires enforcement of mass preservation throughout the computation, in particular in long time scale computations. In the proposed approach, the conservation property is achieved by local mesh intersection and quadrature formulae. Derivatives reconstruction is used to obtain a second order method. Algorithmically, our goal is to design a method which is robust and efficient. The robustness is mandatory to obtain a reliable method on real-life applications and to apply the operator to highly anisotropic meshes. The efficiency is achieved by designing a matrix-free operator which is highly parallel. A multi-thread parallelization is given in this work. Several numerical examples are presented to illustrate the efficiency of the proposed approach