Search results

We describe a new mathematical approach for deriving and solving covolume models of the three‐dimensional, incompressible Navier—Stokes flow equations. The approach integrates three technical components into a single modelling algorothm: automatic grid generation; covolume equation generation; dual variable reduction.

We describe a novel mathematical approach to deriving and solving covolume models of the incompressible 2‐D Navier‐Stokes flow equations. The approach integrates three technical components into a single modelling algorithm: 1. Automatic Grid Generation. An algorithm is described and used to automatically discretize the flow domain into a Delaunay triangulation and a dual Voronoi polygonal tessellation. 2. Covolume Finite Difference Equation Generation. Three covolume discretizations of the Navier‐Stokes equations are presented. The first scheme conserves mass over triangular control volumes, the second scheme over polygonal control volumes and the third scheme conserves mass over both. Simple consistent finite difference equations are derived in terms of the primitive variables of velocity and pressure. 3. Dual Variable Reduction. A network theoretic technique is used to transform each of the finite difference systems into equivalent systems which are considerably smaller than the original primitive finite difference system.

The extended Delaunay tessellation (EDT) is presented in this paper as the unique partition of a node set into polyhedral regions defined by nodes lying on the nearby Voronoï spheres. Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems). The reason for this limitation was the lack of any acceptable shape function to be used in other kind of geometrical elements. Nowadays, there are several acceptable shape functions for a very large class of polyhedra. These new shape functions, together with the EDT, gives an optimal combination and a powerful tool to solve a large variety of physical problems by numerical methods. The domain partition into polyhedra presented here does not introduce any new node nor change any node position. This makes this process suitable for Lagrangian problems and meshless methods in which only the connectivity information is used and there is no need for any expensive smoothing process.

While working with clients in the last years of his life, Gordon Pask produced an axiomatic scheme for his Interactions of Actors Theory which is a development of his well known Conversation Theory. These axioms are interpretable as a general theory of self‐organisation and are discussed as characteristic of field concurrence and as part of the second‐order cybernetics canon. An application to population density is reported supported by both kinematic and kinetic simulation. Implications for cardiovascular anti‐coagulation therapy and planetary evolution are discussed.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.