A technique of reinitialization for efficient simulation of large aquifers using the Discrete Kernel Approach

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Abstract
The numerical technique of finite differences is commonly used to solve the partial differential equation describing saturated flow in aquifers (Boussinesq equation). This technique uses the known initial conditions at the beginning of the time step and the net excitations acting on the aquifer during the time step to compute the unknown heads at the end of the time step. This procedure requires the solution of a generally large system of simultaneous equations (equal to the number of nodes) at each simulation time step. Such an operation may become very costly for types of management problems where generally large aquifers have to be simulated numerous times at short time steps for a long time horizon. A technique which uses the discrete kernel approach and which requires the solution of the saturated flow equation for a small scanning grid system for a few time steps is presented. These solutions for few periods are used to simulate the heads in the total aquifer for long time horizons by a simple discrete convolution. The capability of the technique to handle point excitations and to predict point aquifer drawdowns are demonstrated. A cost comparison is made between the use of this technique and the conventional finite difference technique to solve a test aquifer simulation problem.