An unsplit, higher order Godunov method for scalar conservation laws in multiple dimensions
Journal of Computational Physics
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Godunov-mixed methods for advection-diffusion equations in multidimensions
SIAM Journal on Numerical Analysis
A characteristics-mixed finite element method for advection-dominated transport problems
SIAM Journal on Numerical Analysis
Flux-based methods of characteristics for coupled transport equations in porous media
Computing and Visualization in Science
A Family of Rectangular Mixed Elements with a Continuous Flux for Second Order Elliptic Problems
SIAM Journal on Numerical Analysis
Computing and Visualization in Science
A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows
Journal of Computational Physics
A Fully Mass and Volume Conserving Implementation of a Characteristic Method for Transport Problems
SIAM Journal on Scientific Computing
Journal of Computational Physics
Convergence of a Fully Conservative Volume Corrected Characteristic Method for Transport Problems
SIAM Journal on Numerical Analysis
An Eulerian-Lagrangian WENO finite volume scheme for advection problems
Journal of Computational Physics
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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.