Log-Conformation Representation of Hiperbolic Conservation Laws with Source Term

Luciene Aparecida Bielça Silva, Messias Meneguette


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).


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.

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

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.

Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


Indexed in:




Desenvolvido por:

Logomarca da Lepidus Tecnologia