A Mass Conservative Method for Numerical Modeling of Axisymmetric flow

In this paper, the cell-centered finite volume method (CC-FVM) has been presented to simulate the axisymmetric radial flow toward a pumping well. The model is applied to the unstructured triangular grids which allows to simulate inhomogeneous and complex-shaped domains. Due to the non-orthogonality of the irregular grids, the multipoint flux approximation (MPFA) methods are used to discretize the flux term. In this work, the diamond scheme as the MPFA method has been employed and the least square method is used to interpolate hydraulic head at the vertices in terms of the cell-center values. The numerical scheme has been verified via the Theis solution , as a milestone in well hydraulics. The numerical results show the performance of the model in simulating transient drawdown in the confined aquifers. The proposed numerical model benefits from stability and local conservation contrary to the standard finite element methods. Also this numerical technique has the second order of accuracy.