Log-conformation representation of hiperbolic conservation laws with source term

摘要

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