Abstract:
In the existing finite difference method, the flow (inflow/outflow) is assumed to follow a linear variation with time where as the spatial variation is non-linear and quadratic in nature. In case of a non-homogeneous, semi-infinite aquifer bounded by a fully penetrating stream, the flow rate at the -boundary subsequent to a sudden change in boundary head varies inversely to a square root of time. Therefore the variation of flow at any section can be presumed to be non-linear with time. In improved finite difference scheme, non-linear temporal variation i.e. quadratic in nature has been taken in account. Further in a non-homogeneous case the head variation is sharp within small distance. Therefore a spatial variation may follow a polynomial equation of higher degree. This spatial variation is also accounted in Improved finite difference method. Thus proposed fmite difference method that includes both temporal and spatial variation in consideration may give efficient results.
All numerical methods exhibit oscillations in computed head. This oscillation is prominent at grids adjacent to the boundary. In all these methods, inflow is not accounted truly. The oscillation can be minimized if the inflow is properly accounted for..
