Event Type:

Department Colloquium

Date/Time:

Tuesday, October 25, 2005 - 08:00

Location:

Kidd 364

Guest Speaker:

Institution:

Division of Mathematical Sciences, National Science Foundation

Abstract:

The Eulerian-Lagrangian localized adjoint method (ELLAM) was originally developed for linear advection-diffusion equations. It has no CFL condition, handles all kinds of boundary conditions rigorously, is fully mass-conservative, and its Lagrangian step symmetrizes the advection-diffusion operator. We present here a natural adjoint formulation that extends ELLAM to multiphase multicomponent flows with nonlinear fluxes [1]. This is based on a physical interpretation of the dual adjoint operator as a propagator of mass-carrying particles, in contrast to the wave-propagating primal direct operator. The adjoint operator is linear, so that its space-time characteristics do not intersect, shocks do not form, and particles do not disappear. This makes the dual framework substantially more tractable computationally. All of these concepts are illustrated in some examples and in the discretization of a compositional model.

[1] T.F. Russell, B.O. Heimsund, H.K. Dahle, and M.S. Espedal: Adjoint methods are particle methods. In preparation, 2005.