Unstructured Mesh Generation and Adaptation

Loseille, Adrien

doi:10.1016/bs.hna.2016.10.004

Cited by 21 publications

(15 citation statements)

References 78 publications

(102 reference statements)

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“…To strike a balance, about 10 meshes of

Γ

are created, with uniform and decreasing mesh size. For a given frequency

s (ξ_{k})

, the associated BEM problem is solved using the least refined mesh that has at least 8 points per wavelength, and the BEM solutions obtained on that mesh are interpolated to a master mesh (chosen for postprocessing, or in the future for fluid‐structure coupling) using the software feflo.a 46 …”

Section: Improvements Of the Procedures For Rapid Transient Problemsmentioning

confidence: 99%

A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

Mavaleix-Marchessoux

Bonnet

Chaillat

et al. 2020

Numerical Meth Engineering

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Three-dimensional (3D) rapid transient acoustic problems are difficult to solve numerically when dealing with large geometries, because numerical methods based on geometry discretization (mesh), such as the boundary element method (BEM) or the finite element method (FEM), often require to solve a linear system (from the spacial discretization) for each time step. We propose a numerical method to efficiently deal with 3D rapid transient acoustic problems set in large exterior domains. Using the -transform and the convolution quadrature method, we first present a straightforward way to reframe the problem to the solving of a large amount (the number of time steps, M) of frequency-domain BEMs. Then, taking advantage of a well-designed high-frequency approximation, we drastically reduce the number of frequency-domain BEMs to be solved, with little loss of accuracy. The complexity of the resulting numerical procedure turns out to be O(1) in regard to the time discretization and O(N log N) for the spacial discretization, the latter being prescribed by the complexity of the used fast BEM solver. Examples of applications are proposed to illustrate the efficiency of the procedure in the case of fluid-structure interaction: the radiation of an acoustic wave into a fluid by a deformable structure with prescribed velocity and the scattering of an abrupt wave by simple and realistic geometries.

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“…To strike a balance, about 10 meshes of

Γ

are created, with uniform and decreasing mesh size. For a given frequency

s (ξ_{k})

Section: Improvements Of the Procedures For Rapid Transient Problemsmentioning

confidence: 99%

A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

Mavaleix-Marchessoux

Bonnet

Chaillat

et al. 2020

Numerical Meth Engineering

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“…Tessellation inside elements. Based on these estimators (6), (7) and (8), the TessLevelInner is then set:…”

Section: Control Of the Granularity Of The Tessellationmentioning

confidence: 99%

“…First, a model of the studied objects is generated using a CAD (Computer-Aided Design) model [1]. Surface [2,3] and volume [4,5,6,7] meshes can be deduced from this CAD model. Using meshes, PDEs can be numerically solved with numerical schemes (FDM [8], FEM [9], FVM [10], DG-FEM [11], .…”

Section: Introductionmentioning

confidence: 99%

On pixel-exact rendering for high-order mesh and solution

Feuillet

Maunoury

Loseille

2021

Journal of Computational Physics

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With the increasing use of high-order methods and high-order meshes, scientific visualization software need to adapt themselves to reliably render the associated meshes and numerical solutions. In this paper, a novel approach, based on OpenGL 4 framework, enables a GPU-based rendering of high-order meshes as well as an almost pixel-exact rendering of high-order solutions. Several aspects of the OpenGL Shading Language and in particular the use of dedicated shaders (GPU programs) allows to answer this visualization challenge. Fragment shaders are used to compute the exact solution for each pixel, made possible by the transfer of degrees of freedom and shape functions to the GPU with textures. Tessellation shaders, combined with geometric error estimates, allow us to render high-order curved meshes by providing an adaptive subdivision of elements on the GPU directly. A convenient way to compute bounds for high-order solutions is described. The interest of using Bézier basis instead of Lagrange functions lies in the existence of fast and robust evaluation of polynomial functions with de Casteljau algorithm. A technique to plot highly nonlinear isolines and wire frames with a desired thickness is derived. It is based on a finite difference scheme performed on GPU. In comparison with standard techniques, we remove the use of any linear interpolation step and the need to generate a priori a fixed subdivided mesh. This reduces the memory footprint, improves the accuracy and the speed of the rendering. Finally, the method is illustrated with various 3D examples.

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“…Feflo.a is an adaptation code developed at INRIA. It is based on a two-step procedure to output a unit grid [25,26]. The first step aims at improving the edge length distribution with respect to the input metric field.…”

Section: E Fefloamentioning

confidence: 99%

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Park

Barral

Ibanez

et al. 2018

2018 AIAA Aerospace Sciences Meeting

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Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6 Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

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Unstructured Mesh Generation and Adaptation

Cited by 21 publications

References 78 publications

A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

A fast boundary element method using the Z‐transform and high‐frequency approximations for large‐scale three‐dimensional transient wave problems

On pixel-exact rendering for high-order mesh and solution

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

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