Two-dimensional transient flow in non-level irrigation basins.

Abstract

Shallow water flow over level and non-level soil surfaces is governed by three partial differential equations accounting for momentum in the X₁- and x₂-directions and conservation of mass. An explicit one-dimensional model using a cell based finite difference scheme was used in an attempt to solve those equations numerically, utilizing the zero-inertia assumption; but stability analysis indicated the scheme to be unstable. An implicit non-linear version of the same scheme proved to be consistent and unconditionally stable. To validate the implicit one-dimensional cell-based zero-inertia model, several test cases were run with an existing one-dimensional grid-based model (i.e. SRFR) and with the proposed one-dimensional cell-based model. The results from existing models compared favorably. Grid-based methods are difficult to solve in two-dimensions. The cell based finite difference scheme was extended to simulate level and non-level basins exhibiting significant variations in two directions. An implicit two-dimensional non-linear scheme was developed, and it proved to be consistent and unconditionally stable. The alternating direction implicit (ADI) method was used to solve the two-dimensional non-linear scheme. One set of equations was used, regardless of solution direction. An iterative solution was developed utilizing the Newton Raphson method. The iterations were stopped when a predefined small residual was achieved. Field data were collected for an irrigation on an irrigated basin in the Gila River Farms, for which significant variations in two directions were observed. Water surface elevations were measured with a double-bubbler and pressure transducer system. The same field conditions were simulated using the two-dimensional implicit zero-inertia model, and the results compared favorably. The two-dimensional implicit zero-inertia model has great potential to simulate fields with any geometrical shape, any inflow and soil surface configurations.