A Control Volume Radial Basis Function Techniques for the Numerical Simulation of Saturated Flows in Semi-confined Aquifer

In this work, a Control Volume Radial Basis Function technique (CV-RBF) is adapted to solve ground water flow in the saturated zone of the semi-confined aquifer. The CV-RBF method differs from classical CV methods in the way that the flux at the cell surfaces is computed. A local RBF interpolation of the field variable is performed at the centres of the cell being integrated and its neighbours. This interpolation is then used to reconstruct the solution and its gradient in the integration points which support the flux computation. In addition, it is required that such interpolation satisfies the governing equation in a certain number of points placed around the cell centres. In this way, the local interpolations become equivalent to local boundary-value problems. The CV-RBF method is combined with a local remeshing technique in order to track the phreatic surface, where the gradients required to satisfy the kinematic condition are computed by the same local RBF interpolations used for the flux computation. The proposed numerical approach is validated in a series of three-dimensional groundwater flow problems where the operations of recharging and extracting water from a semi-confined aquifer are modelled.