Coupling of Navier-Stokes and Richards Equations for Numerical Simulation of Two Phase Surface and Subsurface Flow in Surface Drip Irrigation

Abstract

Water dynamic in wetted volume of soil around emitter is one of the primary information for designing the irrigation systems and management of water and chemical substances. In fact, for particular kind of soil, knowing the evolution and gradual change of the shape of the wetted volume is necessary for estimation of the distance of emitters from each other and irrigation duration. Most of the numerical and analytical models used for prediction of wetting pattern need determining the pounding area from high cost experimental tests. These models predict unreliable results if the discharge of emitter is more than infiltration of soil. In this paper, a new model for coupling surface (Navier-Stokes, VOF) and subsurface flow equations (Richards) is presented. The method can use for simulation of both two phase air-water surface flow along with wetting pattern inside the soil in surface drip irrigation. In this model, Richards equation is discretized with finite volume method and coupled with two phases Navier-Stokes equations based on the new coupling algorithm. To demonstrate the accuracy of the model the results of new method for two different soil texture and discharge are compared with experimental data and numerical results of HYDRUS software. Furthermore, statistical indexes such as mean error and root mean square error and model efficiency are evaluated for the model. The results indicated that the presented model has the high ability in simulation of wetted pattern, and its accuracy is more than HYDRUS software.

Keywords

• drip irrigation
• wetting pattern
• navier- stocks equations
• richards equation
• equations coupling