Stability, monotonicity, maximum and minimum principles, and implementation of the volume corrected characteristic method

摘要

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 "fivespot" 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.