A New Approach to Compute Water Level in Non- hydrostatic Models with Application Capabilities for Open and Porous Media Flows

In recent years, considerable accomplishments were devoted for developing non-hydrostatic models for simulation of water level in open channel flows. The main constraint to develop such models, arises from true definitions of water surface boundary condition. Some costly techniques such as VOF and MAC are used for these purposes. These techniques are confronted with high computational costs as well as durability limitations beside their apt accuracy. Another group of non-hydrostatic models determines the water surface elevation using kinematic equation of free surface. These models are of suitable efficiencies if the water level gradient is negligible. Generally, in such conditions, equal number of cells in column and varied height of cells in surface layer are considered. If water level gradient is high, a considerable parts of flow field are solved in hydrostatic condition which frequently occurs in water level of groundwater.
To overcome these limitations in this research, the number of cells in each column was selected proportionate to varied water level which resulted in considerable improvements of water level and flow field. In fact, this technique falls in between VOF and the kinematic boundary condition of water level calculations. It was observed that the accuracy of this method is higher than the kinematic boundary condition with a lesser computational works and stability limitation than VOF. It is noteworthy to mention that, in wave interaction with porous structure test, with time step 6 times greater than VOF model, the current scheme is stable and considering running time, 480 percent more efficient.
The number of cells in each time increments was adjusted commensurate with water level.
This article details a vertical two dimensional non-hydrostatic model for simultaneous simulation of open flow level and water level in porous media. The governing equations are the developed forms of Navier-Stocks equations which commonly applied to fluid and porous media. These equations were discredited by means of finite volume method in Cartesian coordinates and solved by means of pressure bearing approach. The developed model is capable of solving the pressure field taking the advantages of the kinematic free water level and developed form of Navier-Stocks equations. The standard model of was used to model the turbulence.