Abstract: A coupled two-layer finite volume/finite element
method was proposed for solving dam-break flow problem
over deformable beds. The governing equations consist of the
well-balanced two-layer shallow water equations for the water flow
and a linear elastic model for the bed deformations. Deformations
in the topography can be caused by a brutal localized force or
simply by a class of sliding displacements on the bathymetry.
This deformation in the bed is a source of perturbations, on
the water surface generating water waves which propagate with
different amplitudes and frequencies. Coupling conditions at the
interface are also investigated in the current study and two mesh
procedure is proposed for the transfer of information through the
interface. In the present work a new procedure is implemented at
the soil-water interface using the finite element and two-layer finite
volume meshes with a conservative distribution of the forces at
their intersections. The finite element method employs quadratic
elements in an unstructured triangular mesh and the finite volume
method uses the Rusanove to reconstruct the numerical fluxes. The
numerical coupled method is highly efficient, accurate, well balanced,
and it can handle complex geometries as well as rapidly varying
flows. Numerical results are presented for several test examples of
dam-break flows over deformable beds. Mesh convergence study is
performed for both methods, the overall model provides new insight
into the problems at minimal computational cost.
Abstract: In this paper, we present a fast and efficient mesh coarsening algorithm for 3D triangular meshes. Theis approach can be applied to very complex 3D meshes of arbitrary topology and with millions of vertices. The algorithm is based on the clustering of the input mesh elements, which divides the faces of an input mesh into a given number of clusters for clustering purpose by approximating the Centroidal Voronoi Tessellation of the input mesh. Once a clustering is achieved, it provides us an efficient way to construct uniform tessellations, and therefore leads to good coarsening of polygonal meshes. With proliferation of 3D scanners, this coarsening algorithm is particularly useful for reverse engineering applications of 3D models, which in many cases are dense, non-uniform, irregular and arbitrary topology. Examples demonstrating effectiveness of the new algorithm are also included in the paper.
Abstract: This paper presents a linear-elastic finite element method based flattening algorithm for three dimensional triangular surfaces. First, an intrinsic characteristic preserving method is used to obtain the initial developing graph, which preserves the angles and length ratios between two adjacent edges. Then, an iterative equation is established based on linear-elastic finite element method and the flattening result with an equilibrium state of internal force is obtained by solving this iterative equation. The results show that complex surfaces can be dealt with this proposed method, which is an efficient tool for the applications in computer aided design, such as mould design.
Abstract: Subdivision surfaces were applied to the entire
meshes in order to produce smooth surfaces refinement from coarse
mesh. Several schemes had been introduced in this area to provide a
set of rules to converge smooth surfaces. However, to compute and
render all the vertices are really inconvenient in terms of memory
consumption and runtime during the subdivision process. It will lead
to a heavy computational load especially at a higher level of
subdivision. Adaptive subdivision is a method that subdivides only at
certain areas of the meshes while the rest were maintained less
polygons. Although adaptive subdivision occurs at the selected areas,
the quality of produced surfaces which is their smoothness can be
preserved similar as well as regular subdivision. Nevertheless,
adaptive subdivision process burdened from two causes; calculations
need to be done to define areas that are required to be subdivided and
to remove cracks created from the subdivision depth difference
between the selected and unselected areas. Unfortunately, the result
of adaptive subdivision when it reaches to the higher level of
subdivision, it still brings the problem with memory consumption.
This research brings to iterative process of adaptive subdivision to
improve the previous adaptive method that will reduce memory
consumption applied on triangular mesh. The result of this iterative
process was acceptable better in memory and appearance in order to
produce fewer polygons while it preserves smooth surfaces.