A uni ed multigrid solution technique is presented for solving the Euler and Reynoldsaveraged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the...

We give an overview of multilevel methods, such as V-cycle multigrid and BPX preconditioner, for solving various partial differential equations (including H(grad), H(curl) and H(div) systems) on quasi-uniform meshes and extend them to graded meshes and completely unstructured grids. We first discuss the classical multigrid theory on the basis of the method of subspace correction of Xu and a key...

In this paper we propose a particle-based volume rendering approach for unstructured, three-dimensional, tetrahedral polygon meshes. We stochastically generate millions of particles per second and project them on the screen in real-time. In contrast to previous rendering techniques of tetrahedral volume meshes, our method does not need a prior depth sorting of geometry. Instead, the rendered im...

The issue of boundedness in the discretisation of the convection term of transport equations has been widely discussed. A large number of local adjustment practices has been proposed, including the well-known TVD and NVD families of diierencing schemes. All of those use some sort of an \unboundedness indicator" in order to determine the parts of the domain where intervention in the discretisati...

Generating large 3D unstructured meshes with over 1 billion elements has been a challenging task. Fortunately, for a large class of applications with relatively simple geometries, unstructured octree-based hexahedral meshes provide a good compromise between adaptivity and simplicity. This paper presents recent work on how to extract hexahedral mesh structures from a class of database structures...