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Summary: STABILITY, MONOTONICITY, MAXIMUM AND MINIMUM
PRINCIPLES, AND IMPLEMENTATION OF THE VOLUME
CORRECTED CHARACTERISTIC METHOD
TODD ARBOGAST AND WEN-HAO WANG
Abstract. We consider the volume corrected characteristics-mixed method (VCCMM) for tracer
transport problems. The volume correction adjustment maintains the local volume conservation of
bulk fluids and the numerical convergence of the method. We discuss some details of implementation
by considering the scheme from an algebraic point of view. We show that the volume correction
adjustment is important for stability and necessary for the monotonicity and the maximum and
minimum principles of the method. We also derive a relatively weaker stability property for the
uncorrected characteristic-mixed method (CMM). Some numerical experiments of a quarter "five-
spot" pattern of wells are given to verify our theoretical results and compare the concentration errors
of VCCMM and CMM due to random perturbations set up in the computation of the algorithm.
More numerical tests, including one related to long-time nuclear waste storage, are given to compare
VCCMM with CMM and Godunov's method, showing that VCCMM exhibits no overshoots or
undershoots and less numerical diffusion.
Key words. transport, advection, method of characteristics, Lagrangian method, ELLAM,
local conservation, fully conservative
AMS subject classifications. 35L65, 65M12, 65M25, 76S05
1. Introduction. We consider the problem of incompressible dilute miscible
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