Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: Mesh effect and discretization error estimation

© 2014 John Wiley & Sons, Ltd. Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger-amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger-amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger-amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts.