Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term

Authors

  • Luciene Aparecida Bielça Silva FCT/UNESP - Univ Estadual Paulista, 19060-900 Presidente Prudente, SP, Brazil
  • Messias Meneguette FCT/UNESP - Univ Estadual Paulista, 19060-900 Presidente Prudente, SP, Brazil

DOI:

https://doi.org/10.5540/tema.2014.015.03.0293

Abstract

The objective of this work is to study, through a simpler equation, the statement that the numerical instability associated to the high number of Weissenberg in equations with source term can be resolved by the use of the so called logarithmic representation conformation. We will focus on hyperbolic conservation laws, but more specifically on the advection equation with source term. The source term imposes a necessity of an elastic balance, as well as the CFL convective balance for stability. We will see that the representation of such equation by log-conformation removes the restriction of stability inherent to the elastic balance pointed out by [3] as the cause of high Weissenberg number problem (HWNP).

Author Biographies

Luciene Aparecida Bielça Silva, FCT/UNESP - Univ Estadual Paulista, 19060-900 Presidente Prudente, SP, Brazil

MSc in Computacional and Applied Mathematics, FCT/UNESP

Messias Meneguette, FCT/UNESP - Univ Estadual Paulista, 19060-900 Presidente Prudente, SP, Brazil

Universidade Estadual Paulista Júlio de Mesquita Filho, Faculdade de Ciências e Tecnologia de Presidente Prudente, Depto de Matemática, Estatistica e Computação.
Rua Roberto Simonsen, 305
Centro Educacional
19060-900 - Presidente Prudente, SP - Brasil - Caixa-postal: 467
Telefone: (18) 32295620
Ramal: 5620
Fax: (18) 32295353
URL da Homepage: http://www.fct.unesp.br

References

A. M. Afonso; F. T. Pinho; M. A. Alves, The kernel-conformation constitutive laws. J. Non-Newtonian Fluid Mech., vol. 167-168, pp. 30-37 (2012).

J. A. Cuminato; M. Meneguette, Discretização de equações diferenciais parciais: técnicas de diferenças finitas. SBM, 2013.

R. Fattal; R. Kupferman, Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J. Non-Newtonian Fluid Mech., vol. 126, pp. 23-37, (2005).

B. Koren, A robust upwind discretisation method for advection, diffusion and source terms, In: Numerical Methods for Advection-Diffusion Problems,

C.B.Vreugdenhil; B.Koren, (Ed.), Vieweg, 1993.

R. J. LeVeque, Numerical methods for conservation laws. Birkhauser, 1992.

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Published

2014-01-27

How to Cite

Bielça Silva, L. A., & Meneguette, M. (2014). Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term. Trends in Computational and Applied Mathematics, 15(3), 293–299. https://doi.org/10.5540/tema.2014.015.03.0293

Issue

Vol. 15 No. 3 (2014)

Section

Original Article

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