In this paper, we introduce an extension of Van Leer’s slope limiter for two-dimensional discontinuous Galerkin (DG) methods on arbitrary unstructured quadrangular or triangular grids. The aim is to construct a non-oscillatory shock capturing DG method for the approximation of hyperbolic conservative laws without adding excessive numerical dispersion. Unlike some splitting techniques that are l...

The nite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular nite elements are attractive for ocean modeling because of their exibility for representing irregular boundaries and for local mesh re nement. A \kriging" interpolator is used for the semi-Lagrangian advection, leading to an acc...

The transmission-line modelling (TLM) method has been widely applied to many areas including electromagnetic and heat conduction problems. Its unstructured version, TLM (UTLM), however, not hitherto fully exploited in thermal diffusion This paper derives detail a UTLM scheme solve the two-dimensional equation numerically based on optimal Delaunay triangular (ODT) mesh.

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinem...

Wavelet-based methods have proven their efficiency for the visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all waveletbased methods is a hierarchy of meshes that satisfies subdivisionconnectivity: this hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree unifor...

The theory and application of numerical methods for unstructured meshes have been improved significantly in recent years. Because the grids can be place arbitrarily in space, unstructured meshes can provide much higher spatial resolution than regular meshes. The built-in nature of mesh adaptivity for unstructured meshes gives one way to simulate highly dynamic, hierarchical problems involving b...

In this follow-up work, we extend the discontinuous Galerkin (DG) methods previously developed on rectangular meshes [18] to triangular meshes. The DG schemes in [18] are both optimally convergent and energy conserving. However, as we shall see in the numerical results section, the DG schemes on triangular meshes only have suboptimal convergence rate. We prove the energy conservation and an err...

The Modified Direct Method (MDM) is an iterative mesh smoothing method for smoothing planar and surface meshes, which is developed from the non-iterative smoothing method originated by Balendran [1]. When smooth planar meshes, the performance of the MDM is effectively identical to that of Laplacian smoothing, for triangular and quadrilateral meshes; however, the MDM outperforms Laplacian smooth...