Curvilinear Mesh Generation for Boundary Layer Problems

Moxey, David; Hazan, M.; Sherwin, Spencer J.; Peiró, Joaquim

doi:10.1007/978-3-319-12886-3_3

Cited by 4 publications

(8 citation statements)

References 18 publications

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“…We note that here we employ discretization (8) where, according to (23), the same numerical flux is used on the boundary like on interior faces and is evaluated between the interior boundary state and a mirrored exterior boundary state. In contrast to that, evaluating normal fluxes at the wall boundary state like in (19) results in a break-down of the solution process for p D 2 before reaching a residual reduction of 10 4 . In the following, we concentrate on the flow solution u h 2 V p h to (8) with (23) obtained for p D 3 at the end of the solution process shown in Figure 8.…”

Section: Higher-order Cfd Computationmentioning

confidence: 98%

“…326 R. HARTMANN AND T. LEICHT and L e .u h / 2 † p h denotes the local lifting operator defined in (11). Furthermore, the diffusive flux e F v in (19) and the corresponding homogeneity tensor e G is modified on adia such that n rT D 0, that is, n e F v .u; ru/ D n e G.u/ru D ² .0; . n/ 1 ; .…”

Section: Discretization At the Wall Boundary Based On Normal Boundarymentioning

confidence: 99%

“…The discretization (8) together with the numerical boundary fluxes (19) has been proposed in References [28,29] and is (asymptotically) adjoint consistent in combination with following discretization of the force coefficients…”

Section: Discretization At the Wall Boundary Based On Normal Boundarymentioning

confidence: 99%

“…Also other research groups work on high‐order unstructured mesh generation for aerodynamic flows: for example, a group at the University of Swansea who solves the linear elasticity equation on purely tetrahedral meshes, Abgrall et al . who solves the linear elasticity equation on triangular and tretrahedral meshes, Persson & Peraire who solve the nonlinear elasticity equation on inviscid tetrahedral meshes, and a group at ICL who create curved meshes for aerodynamic geometries of rather low complexity. But overall, one can state that currently the generation of higher‐order hybrid (mixed‐element) unstructured RANS meshes for aerodynamic configurations of medium or higher complexity are not readily available.…”

Section: Introductionmentioning

confidence: 99%

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Generation of unstructured curvilinear grids and high‐order discontinuous Galerkin discretization applied to a 3D high‐lift configuration

Hartmann

Leicht

2016

Numerical Methods in Fluids

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SUMMARYDiscontinuous Galerkin (DG) methods allow high-order flow solutions on unstructured or locally refined meshes by increasing the polynomial degree and using curved instead of straight-sided elements. However, one of the currently largest obstacles to applying these methods to aerodynamic configurations of medium to high complexity is the availability of appropriate higher-order curved meshes.In this article, we describe a complete chain of higher-order unstructured grid generation and higherorder DG flow solution applied to a turbulent flow around a three-dimensional high-lift configuration. This includes (i) the generation of an appropriately coarse straight-sided mesh; (ii) the evaluation of additional points on the computer-aided design geometry of the curved-wall boundary for defining a piecewise polynomial boundary representation; (iii) a higher order mesh deformation to translate the curvature from the wall boundary into the interior of the computational domain; and (iv) the description of a DG discretization, which is sufficiently stable to allow a flow computation on the resulting curved mesh. Finally, a fourth-order flow solution of the Reynolds-averaged Navier-Stokes and k-! turbulence model equations is computed on a fourth-order unstructured hybrid mesh around the three-dimensional high-lift simulation of wing-flow noise generation configuration.

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Section: Higher-order Cfd Computationmentioning

confidence: 98%

Section: Discretization At the Wall Boundary Based On Normal Boundarymentioning

confidence: 99%

Section: Discretization At the Wall Boundary Based On Normal Boundarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generation of unstructured curvilinear grids and high‐order discontinuous Galerkin discretization applied to a 3D high‐lift configuration

Hartmann

Leicht

2016

Numerical Methods in Fluids

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“…Two well‐known mesh generators in DLR, named SOLAR and Centaur, as well as the open‐source grid generator Gmsh, have dedicated effort on the development of unstructured high‐order mesh generation for aerodynamic applications under the support of IDIHOM and ADIGMA . Besides, other approaches such as isoparametric mappings, untangling through optimization, and agglomeration from fine structured grids were also proposed. However, as mentioned in the works of Geuzaine et al and Johnston and Barnes, although a number of promising tools for high‐order grid generation already exist, this is still a significant gap between their capabilities and those of grid generators for producing RANS grids.…”

Section: Introductionmentioning

confidence: 99%

High‐order curvilinear mesh generation technique based on an improved radius basic function approach

Zhao

et al. 2019

Numerical Methods in Fluids

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Summary A high‐order curvilinear hybrid mesh generation technique is developed for high‐order numerical method (eg, discontinuous Galerkin method) applications to improve the accuracy for problems with curve boundary. The grid generation technique is based on an improved radius basic function (RBF) approach by which the straight‐edge mesh is converted into high‐order curve mesh. Firstly, an initial straight‐edge mesh is prepared by traditional grid generation software. Then, high‐order interpolation points are inserted into the mesh entities such as edges, faces, and cells according to the final demand of mesh order. To preserve the original geometry, the inserted points on solid wall are then projected onto the CAD model using an open source tool “Open Cascade.” Finally, other inserted points in the field near the solid wall are moved to appropriate positions by the improved RBF approach to avoid tangled cells. If we use the original RBF approach, then the inserted points on the edge and face entities normal to the solid boundary in the region of boundary layer will move to improper positions. To overcome this problem, a weighting based on the local grid aspect ratio between normal direction and tangential direction is introduced into the baseline RBF approach. Three typical configurations are tested to validate the mesh generator. Meanwhile, a third‐order solution of subsonic flow over an analytical 3D body of revolution in the second International Workshop on High‐Order CFD Methods is supplied by a discontinuous Galerkin solver. These numerical tests demonstrate the potential capability of present technique for high‐order simulations of complex geometries.

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Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements

et al. 2019

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The under integration of the volume terms in the discontinuous Galerkin spectral element approximation introduces errors at non-conforming element faces that do not cancel and lead to freestream preservation errors. We derive volume and face conditions on the geometry under which a constant state is preserved. From those, we catalog eight constraints on the geometry that preserve a constant state. Numerical examples are presented to illustrate the results.

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Curvilinear Mesh Generation for Boundary Layer Problems

Cited by 4 publications

References 18 publications

Generation of unstructured curvilinear grids and high‐order discontinuous Galerkin discretization applied to a 3D high‐lift configuration

Generation of unstructured curvilinear grids and high‐order discontinuous Galerkin discretization applied to a 3D high‐lift configuration

High‐order curvilinear mesh generation technique based on an improved radius basic function approach

Free-Stream Preservation for Curved Geometrically Non-conforming Discontinuous Galerkin Spectral Elements

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