Stable high-order finite-difference methods based on non-uniform grid point distributions

Hernández Ramos, Juan Antonio y Hermanns Navarro, Miguel (2008). Stable high-order finite-difference methods based on non-uniform grid point distributions. "International Journal For Numerical Methods In Fluids", v. 56 (n. 3); pp. 233-255. ISSN 0271-2091. https://doi.org/10.1002/fld.1510.

Descripción

Título: Stable high-order finite-difference methods based on non-uniform grid point distributions
Autor/es:
  • Hernández Ramos, Juan Antonio
  • Hermanns Navarro, Miguel
Tipo de Documento: Artículo
Título de Revista/Publicación: International Journal For Numerical Methods In Fluids
Fecha: Enero 2008
Volumen: 56
Materias:
Palabras Clave Informales: high-order scheme; finite difference; piecewise polynomials; stability; Runge phenomenon; pseudospectra
Escuela: E.T.S.I. Aeronáuticos (UPM) [antigua denominación]
Departamento: Matemática Aplicada y Estadística [hasta 2014]
Licencias Creative Commons: Reconocimiento - Sin obra derivada - No comercial

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Resumen

It is well known that high-order finite-difference methods may become unstable due to the presence of boundaries and the imposition of boundary conditions. For uniform grids, Gustafsson, Kreiss, and Sundstr¨om theory and the summation-by-parts method provide sufficient conditions for stability. For non-uniform grids, clustering of nodes close to the boundaries improves the stability of the resulting finite-difference operator. Several heuristic explanations exist for the goodness of the clustering, and attempts have been made to link it to the Runge phenomenon present in polynomial interpolations of high degree. By following the philosophy behind the Chebyshev polynomials, a non-uniform grid for piecewise polynomial interpolations of degree q_N is introduced in this paper, where N + 1 is the total number of grid nodes. It is shown that when q = N, this polynomial interpolation coincides with the Chebyshev interpolation, and the resulting finite-difference schemes are equivalent to Chebyshev collocation methods. Finally, test cases are run showing how stability and correct transient behaviours are achieved for any degree q<N through the use of the proposed non-uniform grids. Discussions are complemented by spectra and pseudospectra of the finite-difference operators.

Más información

ID de Registro: 2439
Identificador DC: http://oa.upm.es/2439/
Identificador OAI: oai:oa.upm.es:2439
Identificador DOI: 10.1002/fld.1510
URL Oficial: http://www3.interscience.wiley.com/journal/117868808/issue
Depositado por: Memoria Investigacion
Depositado el: 16 Abr 2010 08:21
Ultima Modificación: 20 Abr 2016 12:08
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