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2015 | 25 | 3 | 529-537
Tytuł artykułu

A sixth-order finite volume method for the 1D biharmonic operator: Application to intramedullary nail simulation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for onedimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.
Rocznik
Tom
25
Numer
3
Strony
529-537
Opis fizyczny
Daty
wydano
2015
otrzymano
2013-10-21
poprawiono
2014-07-31
Twórcy
  • Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
  • Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
  • Centre of Mathematics, University of Minho, Campus de Azurém, 4800-058 Guimarães, Portugal
  • Institute of Mathematics, Paul Sabatier University, 118, route de Narbonne, 31062 Toulouse, France
Bibliografia
  • Audusse, E. and Bristeau, M.-O. (2007). Finite-volume solvers for a multilayer Saint-Venant system, International Journal of Applied Mathematics and Computer Science 17(3): 311-320, DOI: 10.2478/v10006-007-0025-0.
  • Barreira, L., Teixeira, C. and Fonseca, E. (2008). Avaliação da resistência do colo do fémur utilizando o modelo de elementos finitos, Revista da Associação Portuguesa de Análise Experimental de Tensões 16: 19-24.
  • Branco, C.M. (2011). Mecgnica dos Materiais, Fundação Calouste Gulbenkian, Lisboa.
  • Clain, S., Diot, S. and Loubère, R. (2011). A high-order polynomial finite volume method for hyperbolic system of conservation laws with multi-dimensional optimal order detection (MOOD), Journal of Computational Physics 230(10): 4028-4050.
  • Clain, S., Machado, G.J., Nóbrega, J.M. and Pereira, R.M.S. (2013). A sixth-order finite volume method for the convection-diffusion problem with discontinuous coefficients, Computer Methods in Applied Mechanics and Engineering 267(1): 43-64.
  • Diot, S., Clain, S. and Loubère, R. (2011). Multi-dimensional optimal order detection (mood)-a very high-order finite volume scheme for conservation laws on unstructured meshes, 6th Finite Volume and Complex Application, Prague, Czech Republic, pp. 263-271.
  • Dumbser, M. and Munz, C.-D. (2007). On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes, International Journal of Applied Mathematics and Computer Science 17(3): 297-310, DOI: 10.2478/v10006-007-0024-1.
  • Eymard, R., Gallouët, T. and Herbin, R. (2000). The finite volume method, in P. Ciarlet and J.L. Lions (Eds.), Handbook for Numerical Analysis, North Holland, Amsterdam, pp. 715-1022.
  • Hernández, J. (2002). High-order finite volume schemes for the advection-diffusion equation, International Journal for Numerical Methods in Engineering 53(5): 1211-1234.
  • Kroner, D. (1997). Numerical Schemes for Conservation Laws, Wiley-Teubneur Publishers, Chichester.
  • Leveque, R.J. (2002). Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge.
  • Ollivier-Gooch, C. and Altena, M.V. (2002). A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation, Journal of Computational Physics 181(2): 729-752.
  • Ramos, A. and Simoes, J.A. (2009). Caracterização de cavilhas de fixação intra-medular de estabilização de fracturas ósseas, Revista da Associação Portuguesa de Análise Experimental de Tensões 17: 49-55.
  • Toro, E. (2009). Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, Berlin/Heidelberg.
  • Toro, E. and Hidalgo, A. (2009). Ader finite volume schemes for nonlinear reaction-diffusion equations, Applied Numerical Mathematics 59(1): 73-100.
  • Trangenstein, J.A. (2009). Numerical Solution of Hyperbolic Partial Differential Equations, Cambridge University Press, Cambridge.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv25i3p529bwm
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