A Mass Conservative Method for Numerical Modeling of Axisymmetric flow

Abstract

In this paper, the axisymmetric flow toward a pumping well has been numerically solved by the cell-centered finite volume method. The numerical model is descretized over unstructured and triangular-shaped grids which allows to simulate inhomogeneous and complex-shaped domains. Due to the non-orthogonality of the irregular grids, the multipoint flux approximation (MPFA) schemes 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 applied to express the full discrete form of the vertex-values of the hydraulic head. The scheme has been verified via the Theis solution, as a milestone in well hydraulics. The numerical results show the capability of the developed model in evaluating transient drawdown in the confined aquifers. The proposed numerical model leads to the stable and local conservative solutions contrary to the standard finite element methods. Also this numerical technique has the second order of accuracy.