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Article Content:-
Abstract
Robust, accurate and efficient numerical simulation of groundwater flow in the unsaturated zone remains computationally expensive, particularly for problems that involved sharp fronts in both space and time. Numerical solution of these problems along with standard approaches that use of uniform spatial and temporal discretizations leads to inefficient and expensive simulations. Accurate solution of pressure head form of Richards' equation is very difficult using standard time integration techniques because in the time integration process the mass balance errors grows unless very small time steps are used. Richards' equation may be solved for many problems more economically and robustly with variable time step size instead of constant time step size. We solve Richards' equation using the method of lines with a standard finite difference technique. We show how a differential algebraic equation implementation of the method of lines can give solutions to Richards' equation that are accurate, have good mass balance properties, and are more economical for a wide range of solution accuracy. We implement the method of lines using four higher order time integration MATLAB ODE solvers ode15s, ode23s, ode23t and ode23tb to (i) assure robustness for difficult nonlinear problems and computational efficiency; (ii) develop higher order adaptive methods for the time; (iii) investigate the advantage of using higher-order methods in time; and (iv) compare the computational performance of the ODE solvers. The numerical results demonstrate that the proposed method provides a robust and efficient alternative to standard approaches for simulating variably saturated flow in one spatial dimension.
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