Finite Volume Solution of Flow in Steep Slope Canals Using Triangular Unstructured Mesh

Associate mathematical model for solving super critical free surface flows in canals with steep bed slope in certain direction is introduced in present paper. The developed model consists of depth averaged equations for flow on surface with steep toward one of the main horizontal axes of Cartesian coordinates. The depth-averaged from of the flow equations converted to discrete from for unstructured meshes using the cell vertex finite volume methods. Therefore, the horizontal mesh is firstly transformed into inclined coordinate system. Then discrete formulations are solved on the transformed mesh. Having computes the velocity vector parallel to the bed surface and flow depth perpendicular to the bed surface, the model computes three components of the velocity in Cartesian coordinate system as well as the water depths parallel to the z axe in vertical direction. The develop model is utilized simulation of various flow regimes in prismatic canals, which have two different constant bed slopes in certain direction. The numerical results present the ability of the model to similar very high speed super – critical flows in very steep bed slops. Finally , application of the developed model simulation of super critical flow in gated chute spillway of Aviemore dam in New Zealand with 1:1 bed slope produced encouraging results.

Keywords:

Depth Averaged , Super Critical Flow , Steep Slope Chute , Unstructured Finite Volumes