 
Summary: SIAM J. SCI. COMPUT. c 2006 Society for Industrial and Applied Mathematics
Vol. 28, No. 6, pp. 20012022
A FULLY MASS AND VOLUME CONSERVING
IMPLEMENTATION OF A CHARACTERISTIC METHOD
FOR TRANSPORT PROBLEMS
TODD ARBOGAST AND CHIEHSEN HUANG
Abstract. The characteristicsmixed method considers the transport not of a single point or
fluid particle, but rather the mass in an entire region of fluid. This mass is transported along the char
acteristic curves of the hyperbolic part of the transport equation, and the scheme thereby produces
very little numerical dispersion, conserves mass locally, and can use long time steps. However, since
the shape of a characteristic traceback region must be approximated in numerical implementation,
its volume may be incorrect, resulting in inaccurate concentration densities and, further, inaccurate
reaction dynamics. We present a simple modification to the characteristicsmixed method that con
serves both mass and volume of the transported fluid regions. Our algorithm also handles boundary
conditions through a spacetime change of variables in the traceback routines, which allows the
boundary to be treated as if it were interior to the domain. Nearly point sources, such as wells,
present special difficulties, since characteristic traceback curves converge in their vicinity. We also
present techniques that allow one to conservatively implement wells. The techniques are illustrated
in five numerical examples.
Key words. advectiondiffusion, characteristicsmixed method, ELLAM, mixed finite element,
