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SIAM J. SCI. COMPUT. c 2006 Society for Industrial and Applied Mathematics Vol. 28, No. 6, pp. 20012022
 

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 CHIEH-SEN HUANG
Abstract. The characteristics-mixed 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 trace-back 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 characteristics-mixed method that con-
serves both mass and volume of the transported fluid regions. Our algorithm also handles boundary
conditions through a space-time change of variables in the trace-back 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 trace-back 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. advection-diffusion, characteristics-mixed method, ELLAM, mixed finite element,

  

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

 

Collections: Mathematics; Geosciences