Viscous Meshes Research Articles

AUTOMATIC VISCOUS BOUNDARY LAYER MESH GENERATION

High Reynolds number fluid flows have boundary layers at the wall. To automatically generate robust and valid boundary layer mesh for the simulations is still the bottleneck problem of computational fluid dynamics. Prisms/Tetrahedra hybrid mesh leads to significant savings in mesh size and solution costs. However, it's still difficult to generate prismatic elements of high quality within boundary layers of complex models. Previous advancing layers techniques sometimes lead to invalid meshes and poor quality elements at concave/convex ridges and sharp corners. To improve these situations, we present a strategy for automatically generating viscous boundary layer mesh. In this method, multiple growth directions at ridges and corners are well defined by the dihedral angles around the vertices and the growth heights are adjusted appropriately. Therefore, boundary layer mesh grows well at sharp corners, convex and concave ridges of the domain. We also decrease the number of global intersection checks by predefining the total growth heights before generating elements through one global check, which improves the efficiency of mesh generation. At the same time, we develop a 3D strategy of mesh size control to get a size uniform triangular mesh of the outer boundary of the boundary layer mesh, which is beneficial to generate far-field isotropic mesh of high quality. Finally, mesh examples and the viscous flow simulations including 2D and 3D are presented. In 3D, the hybrid mesh over the standard ONERA M6 and DLR-F6 configurations are generated with the present method. The numerical results agree very well with experiment data which indicates that the hybrid viscous meshes generated by the proposed method are effective and efficient.

A discontinuous Galerkin scheme for Chimera overset viscous meshes on curved geometries

The Chimera overset method is a powerful technique for modeling fluid flow associated with complex engineering problems. The use of structured meshes has enabled engineers to develop a number of high-order schemes, such as the WENO and compact differencing schemes. This paper demonstrates a Discontinuous Galerkin (DG) scheme with a Chimera overset method applied to viscous meshes on curved geometries. The small stencil of the DG scheme makes it particularly suitable for Chimera meshes. The small stencil simplifies the hole cutting and partitioning of grids that contain holes. In addition, because the DG scheme represents the solution as cell local polynomials, it does not require an interpolation scheme with a large stencil to establish the inter-grid communication in overlapping regions. Furthermore, the DG scheme is capable of using curved cells to represent geometric features. The curved cells resolve issues associated with linear non-co-located Chimera viscous meshes used for finite volume and finite difference schemes. The DG-Chimera method is demonstrated on a set of viscous Chimera meshes, which would produce erroneous results for a finite volume or finite difference scheme without corrections to the interpolation.

Efficient Mesh Deformation Using Radial Basis Functions on Unstructured Meshes

An efficient mesh-deformation algorithm has been developed within an unstructured-grid computational-fluid-dynamics solver framework based on a radial-basis-function volume-interpolation method. The data-transfer problem between fluid and structural solvers is simplified here using a beam structural representation, with surface mesh deformation given directly via translational and rotational deformations. The volume mesh deformation is then performed using a radial-basis-function method, which requires no mesh-connectivity information and allows straightforward implementation in an unstructured computational-fluid-dynamics solver in a parallel fashion. However, the pure method is impractical for large meshes, and a novel “greedy” data-reduction algorithm is presented here to select an optimum reduced set of surface mesh points, which makes the mesh-deformation method extremely efficient. Several two- and three-dimensional test cases are presented to validate the algorithm performance, including a realistic aircraft Bell M427 main rotor. It is shown that the approach can handle effectively very large mesh deformations of complex geometries using unstructured viscous meshes while maintaining good mesh quality and geometric accuracy, and generally requires less than 25% of the computational-fluid-dynamics flow-solver cost.

A fast mesh deformation method using explicit interpolation

A novel mesh deformation algorithm for unstructured polyhedral meshes is developed utilizing a tree-code optimization of a simple direct interpolation method. The algorithm is shown to provide mesh quality that is competitive with radial basis function based methods, with markedly better performance in preserving boundary layer orthogonality in viscous meshes. The parallelization of the algorithm is described, and the algorithm cost is demonstrated to be O( n log n). The parallel implementation was used to deform meshes of 100 million nodes on nearly 200 processors demonstrating that the method scales to large mesh sizes. Results are provided for a simulation of a high Reynolds number fluid–structure interaction case using this technique.

Unstructured Viscous Layer Insertion Using Linear-Elastic Smoothing

A robust scheme for generating unstructured viscous meshes, using elliptic partial differential smoothing, is presented. Linear-elasticity relationships, borrowed from the structural mechanics discipline, provide the governing partial differential equations for smoothly displacing the existing mesh, making room for new viscous layers. These viscous layers are allowed to advance up adjacent, nonviscous boundaries. A process of inserting layers on alternating boundary groupings enables the creation of high-quality hexahedral elements in juncture regions. Viscous layer height is allowed to vary, depending on the size of the local inviscid mesh. Three-dimensional results are included to illustrate the use of the method to produce high-quality viscous meshes.

Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation

A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.