A Fully Mass and Volume Conservating Implementation of A Characteristic Method for Transport problems

Todd Arbogast (Department of Mathematics, The University of Texas at Austin)   Chieh-Sen Huang (Department of Mathematics, National Sun Yat-Sen University)
The characteristics-mixed method minimizes numerical dispersion, uses long time steps, and conserves mass locally. Since traceback regions are approximated, their volume may be incorrect, resulting in inaccurate concentration densities and reaction dynamics. We present a simple scheme that conserves both mass and volume, and a conservative implementation of boundary conditions and wells. A space-time change of variables in the traceback routines allows the boundary to be treated as if it were interior to the domain.