 
Summary: A FULLY CONSERVATIVE EULERIANLAGRANGIAN METHOD
FOR A CONVECTIONDIFFUSION PROBLEM
IN A SOLENOIDAL FIELD
TODD ARBOGAST AND CHIEHSEN HUANG
Abstract. Tracer transport is governed by a convectiondiffusion problem modeling mass conser
vation of both tracer and ambient fluids. Numerical methods should be fully conservative, enforcing
both conservation principles on the discrete level. Locally conservative characteristics methods con
serve the mass of tracer, but may not conserve the mass of the ambient fluid. In a recent paper by the
authors [A fully mass and volume conserving implementation of a characteristic method for trans
port problems, SIAM J. Sci. Comput., 28 (2006), pp. 20012022], a fully conservative characteristic
method, the Volume Corrected Characteristics Mixed Method (VCCMM), was introduced for poten
tial flows. Here we extend and apply the method to problems with a solenoidal (i.e., divergencefree)
flow field. The modification is a computationally inexpensive simplification of the original VCCMM,
requiring a simple adjustment of traceback regions in an elementbyelement traversal of the domain.
Our numerical results show that the method works well in practice, is less numerically diffuse than
uncorrected characteristic methods, and can use up to at least about eight times the CFL limited
time step.
Key words. advectiondiffusion, characteristics, local conservation, ELLAM, cellular flow,
divergencefree flow, convectionenhanced diffusion
1. Introduction. We consider the numerical approximation of a convection
