Do we know WENO?

  • Date: 03/21/2008

Ray Spiteri (University of Saskatchewan)


University of British Columbia


The weighted essentially non-oscillatory (WENO) methods are popular
spatial discretization methods for hyperbolic partial differential
equations. In this talk I show that the combination of the widely used
fifth-order WENO spatial discretization (WENO5) and several of the most
popular time integration methods are in fact linearly unstable (and
hence not convergent) when numerically integrating hyperbolic
conservation laws. We find that a sufficient condition for the
combination of an explicit Runge-Kutta (ERK) method and WENO5 to be
linearly stable is that the linear stability region of the ERK method
should include the part of the imaginary axis of the form [-mu,mu], for
some mu>0. The linear stability analysis also provides insight (and
busts some myths) about the behaviour of ERK methods applied to
nonlinear problems and problems with discontinuous solutions. We
confirm the predictions of our analysis by means of numerical tests.

Other Information: 

SCAIM Seminar 2006