Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
A FULLY CONSERVATIVE EULERIAN-LAGRANGIAN METHOD FOR A CONVECTION-DIFFUSION PROBLEM
 

Summary: A FULLY CONSERVATIVE EULERIAN-LAGRANGIAN METHOD
FOR A CONVECTION-DIFFUSION PROBLEM
IN A SOLENOIDAL FIELD
TODD ARBOGAST AND CHIEH-SEN HUANG
Abstract. Tracer transport is governed by a convection-diffusion 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., divergence-free)
flow field. The modification is a computationally inexpensive simplification of the original VCCMM,
requiring a simple adjustment of trace-back regions in an element-by-element 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. advection-diffusion, characteristics, local conservation, ELLAM, cellular flow,
divergence-free flow, convection-enhanced diffusion
1. Introduction. We consider the numerical approximation of a convection-

  

Source: Arbogast, Todd - Center for Subsurface Modeling & Department of Mathematics, University of Texas at Austin

 

Collections: Mathematics; Geosciences