We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a strict maximum principle for general nonlinear convection-diffusion equations on unstructured triangular meshes. Motivated by genuinely high order maximum-principle-satisfying DG schemes for hyperbolic conservation laws [14, 26], we prove that under suitable time step restriction for forward Euler time stepping...

The accuracy of the least-squares technique for gradient reconstruction on unstructured meshes is examined. While least-squares techniques produce accurate results on arbitrary isotropic unstructured meshes, serious di culties exist for highly stretched meshes in the presence of surface curvature. In these situations, gradients are typically under-estimated by up to an order of magnitude. For v...

4 Unstructured meshes are common in coastal modeling, but still rarely used 5 for modeling the large-scale ocean circulation. Existing and new projects 6 aim at changing this situation by proposing models enabling a regional 7 focus (multiresolution) in global setups, without nesting and open bound8 aries. Among them, finite-volume models using the C-grid discretization on 9 Voronoi-centroidal ...

In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a sell avoiding walk which can be applied t...

We consider in this work the numerical resolution of a 2D shallow water system with Coriolis effect and bottom friction stresses on unstructured meshes by new Finite Volume Characteristics (FVC) scheme, which has been introduced preliminary works that will be cited below. Our main goal is to extend approach formalism while preserving physical mathematical properties system, including C-property...

Abstract Fourier spectra are powerful tools to analyze the scale behavior of turbulent flows. While such mathematically based on regular periodic data, some state‐of‐the‐art ocean and climate models use unstructured triangular meshes. Observational data is often also available only in an fashion. In this study, analysis specifically for output with meshes discussed representable wavenumbers der...

This paper presents some linear adaptive non-nested multigrid methods which are applied to linear elastic problems discretized with triangular and tetrahedral nite elements using unstructured and Delaunay mesh generators. The Zienkiewicz-Zhu error estimator and a h-re nement procedure are used to obtain the non-nested meshes used by the multigrid methods. We solve problems with a speci ed perce...

Several performance improvements for finite-element edge-based sparse matrix–vector multiplication algorithms on unstructured grids are presented and tested. Edge data structures for tetrahedral meshes and triangular interface elements are treated, focusing on nodal and edges renumbering strategies for improving processor and memory hierarchy use. Benchmark computations on Intel Itanium 2 and P...