Delaunay triangulation in computational fluid dynamics

AbstractA method, which utilises the Delaunay criterion, is described by which computational grids consisting of assemblies of triangles or tetrahedra can be constructed. An algorithm is briefly outlined to construct the triangulation and its dual, the Voronoi diagram. Issues related to how to construct boundary conforming grids from such a triangulation are addressed, and details are presented of how grid points within the domain can be generated automatically. The point generation algorithm utilises either the given boundary point distribution, or, for grid adaption, a background mesh. Computational aspects of constructing the triangulation in both 2 and 3 dimensions are covered. Examples of meshes and flow computations for a range of aerospace geometries are presented

Stability Analysis of Galerkin/Runge-Kutta Navier-Stokes Discretisations on Unstructured Grids

This paper presents a timestep stability analysis for a class of discretisations applied to the linearised form of the Navier-Stokes equations on a 3D domain with periodic boundary conditions. Using a suitable definition of the `perturbation energy' it is shown that the energy is monotonically decreasing for both the original p.d.e. and the semi-discrete system of o.d.e.'s arising from a Galerkin discretisation on a tetrahedral grid. Using recent theoretical results concerning algebraic and generalised stability, sufficient stability limits are obtained for both global and local timesteps for fully discrete algorithms using Runge-Kutta time integration

Yee's scheme for the integration of Maxwell's equation on unstructured meshes

The co-volume integration method, Yee\u92s scheme, generalized to unstructured mesh is considered and compared with time domain finite element method (TDFE). In order to generate the meshes for which a good quality dual mesh is ensured, a new point placing method for the generation of meshes appropriate for the use of the co-volume method is proposed. Numerical examples are presented which demonstrate the consistency and performance of the co-volume method

Solution Adaptive Unstructured Grid Generation Using Pseudo-Pattern Recognition Techniques

A procedure is presented for anisotropic adaptation of inviscid type flow features with CFD simulation using an unstructured grid. The basic grid generation scheme is an existing advancing--front, local--reconnection (AFLR) procedure. This procedure is modified to allow the field point spacing and alignment to vary based on a flow field solution using adaptive grid regeneration. Multiple physically based feature detectors are used to isolate regions in the field which contain physical features of interest. Using pattern recognition techniques, these regions are reduced to groups of simple geometric entities representing the physical features. Features such as expansion or stagnation regions are reduced to singular points. Shock waves and contact discontinuities are reduced to curves. In the adaptive grid regeneration procedure, singular points are treated as adaptive sources which modify the boundary and field point spacing. Curves are treated as embedded boundaries. These embedded dua..

An investigation in to the use of hybrid structured-unstructured meshes in computational aerodynamics Part II; mesh generation

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