This paper describes an algorithm for generating unstructured triangular meshes from a continuous two-dimensional object represented by an image. The algorithm uses squares as a background grid from which to build the quadrilateral elements that conform to the input contours. Then the triangulation is obtained by automatically choosing the diagonals that optimize the angles of the triangles. Th...

In this paper we present a new unstructured spectral element method for use on triangular and tetrahedral subdomains. The algorithm maintains the accuracy and efficiency of standard quadrilateral/hexahedral spectral element methods but offers greater adaptivity. Standard unstructured meshes can be used and the order of the polynomial expansion can be varied within each triangular/tetrahedral su...

In the present paper, we introduce theH-wavelet method for the fast solution of nonlocal operator equations on unstructured meshes. On the given mesh, we construct a wavelet basis which provides vanishing moments with respect to the traces of polynomials in the space. With this basis at hand, the system matrix in wavelet coordinates is compressed to O(N logN) relevant matrix coefficients, where...

Over the years, multigrid has been demonstrated as an efficient technique for solving inviscid flow problems. However, for viscous flows, convergence rates often degrade. This is generally due to the required use of stretched meshes (i.e., the aspect ratio AR = ∆y/∆x << 1) in order to capture the boundary layer near the body. Usual techniques for generating a sequence of grids that produce prop...

Classic Cartesian staggered mesh schemes have a number of attractive properties. They do not display spurious pressure modes and they have been shown to locally conserve, mass, momentum, kinetic energy, and circulation to machine precision. Recently, a number of generalizations of the staggered mesh approach have been proposed for unstructured (triangular or tetrahedral) meshes. These unstructu...

We have recently introduced a new cell-centered Lax-Wendroff HLL hybrid scheme for Lagrangian hydrodynamics [Fridrich et al. J. Comp. Phys. 326 (2016) 878-892] with results presented only on logical rectangular quadrilateral meshes. In this study we present an improved version unstructured meshes, including uniform triangular and hexagonal meshes non-uniform polygonal The performance of the is ...

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...

A higher-order mimetic method for the solution of partial differential equations on unstructured meshes is developed and demonstrated on the problem of conductive heat transfer. Mimetic discretization methods create discrete versions of the partial differential operators (such and the gradient and divergence) that are exact in some sense and therefore mimic the important mathematical properties...

This paper presents a generic approach to generation of surface and volume unstructured meshes for complex free-form objects, obtained by laser scanning. A four-stage automated procedure is proposed for discrete data sets: surface mesh extraction from Delaunay tetrahedrization of scanned points, surface mesh simplification, definition of triangular interpolating subdivision faces, Delaunay volu...

In this paper we generalize a new type of compact Hermite weighted essentially nonoscillatory (HWENO) limiter for the Runge-Kutta discontinuous Galerkin (RKDG) methods, which were recently developed in [34] for structured meshes, to two dimensional unstructured triangular meshes. The main idea of this limiter is to reconstruct the new polynomial using the entire polynomials of the DG solution f...