In this paper, we generalize the compact subcell weighted essentially non oscillatory (CSWENO) limiting strategy for Runge-Kutta discontinuous Galerkin method developed recently in [1] structured meshes to unstructured triangular meshes. The main idea of is divide immediate neighbors a given cell as subcells into required stencil and use WENO reconstruction limiting. This can be applied any typ...

In this work we study the propagation problem due to the conformity process in the longestedge based refinement algorithms for triangular unstructured meshes. The geometric properties in study answers the important question of how the size of the triangulation is affected when local refinement is applied. We prove both theoretically and empirically that the propagation of a single triangle refi...

Radiative heat transfer in a complex two-dimensional enclosure with an absorbing, emitting, and isotropically scattering gray medium is investigated by using the finite-volume method. In particular, an implementation of the unstructured polygonal meshes, based on an unstructured triangular system, is introduced, thereby reducing the computation time required for the analysis of thermal radiatio...

We present a two-dimensional, well-balanced, central-upwind scheme for approximating solutions of the shallow water equations in the presence of a stationary bottom topography on triangular meshes. Our starting point is the recent central scheme of Kurganov and Petrova (KP) for approximating solutions of conservation laws on triangular meshes. In order to extend this scheme from systems of cons...

Recently, research originating in several dierent applications has appeared on un-structured triangular meshes in which the vertex distribution is not locally uniform, i.e. anisotropic unstructured meshes. The techniques used have the common features that the distribution of triangle shapes for the mesh is controlled by specifying a symmetric tensor, and that the anisotropic mesh is the transfo...

Most efficient adaptive mesh methods employ only a few strategies, including local mesh refinement (h-adaptation), movement of mesh nodes (r-adaptation), and node reconnection (c-adaptation). Despite of its simplicity, node reconnection is the least popular of the three. However, using only node reconnection the discretization error can be significantly reduced. In this paper, we develop and nu...

The discrete convection-diffusion equations obtained from streamline diffusion finite element discretization are solved on both uniform meshes and adaptive meshes. Estimates of error reduction rates for both geometric multigrid (GMG) and algebraic multigrid (AMG) are established on uniform rectangular meshes for a model problem. Our analysis shows that GMG with line Gauss-Seidel smoothing and b...

This document presents an interpolation operator on unstructured triangular meshes that verifies the properties of mass conservation, P-exactness (order 2) and maximum principle. This operator is important for the resolution of the conservation laws in CFD by means of mesh adaptation methods as the conservation properties is not verified throughout the computation. Indeed, the mass preservation...

This paper presents the development of a 2D solver for inviscid and viscous compressible flows using the spectral difference (SD) method for unstructured grids with mixed elements. A mixed quadrilateral and triangular grid is first refined using one-level h-refinement to generate a quadrilateral grid while keeping the curvature of boundary edges. The SD method designed for quadrilateral meshes ...