• A CELL-CENTERED SECOND-ORDER A...

Result: A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES: A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes.

Title:
A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES: A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes.
Authors:
Bertolazzi, Enrico, G. Manzini
Source:
Mathematical models and methods in applied sciences 14 (2004): 1235–1260. doi:10.1142/S0218202504003611
info:cnr-pdr/source/autori:Bertolazzi E., Manzini G./titolo:A cell-centered second-order accurate finite volume method for convection-diffusion problems on unstructured meshes/doi:10.1142%2FS0218202504003611/rivista:Mathematical models and methods in applied sciences/anno:2004/pagina_da:1235/pagina_a:1260/intervallo_pagine:1235–1260/volume:14
Publisher Information:
World Scientific Pub Co Pte Ltd, 2004.
Publication Year:
2004
Subject Terms:
convergence, Numerical computation of solutions to systems of equations, unstructured meshes, finite volume method, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, advection-diffusion boundary value problems, Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs, 01 natural sciences, Boundary value problems for second-order elliptic equations, convection diffusion equation, 0101 mathematics, fixed point iterative technique, numerical experiments, least squares algorithm
Document Type:
Academic journal Article
File Description:
application/xml; application/pdf
Language:
English
ISSN:
1793-6314
0218-2025
DOI:
10.1142/s0218202504003611
Access URL:
https://www.worldscientific.com/doi/abs/10.1142/S0218202504003611
https://dialnet.unirioja.es/servlet/articulo?codigo=970930
Accession Number:
edsair.doi.dedup.....1a43b13b183199f50f0c3ece9dfd0d62
Database:
OpenAIRE

Further Information

A MUSCL-like cell-centered finite volume method is proposed to approximate the solution of multi-dimensional steady advection–diffusion equations. The second-order accuracy is provided by an appropriate definition of the diffusive and advective numerical fluxes. The method is based on a least squares reconstruction of the vertex values from cell averages. The slope limiter, which is required to prevent the formation and growth of spurious numerical oscillations, is designed to guarantee that the discrete solution of the nonlinear scheme exists. Several theoretical issues regarding the solvability of the resulting discrete problems are thoroughly discussed. Finally, numerical experiments that validate the effectiveness of the approach are presented.