The Effect of Methods of Calculating Velocity on Cell Faces in Sub-critical Open Channel Flow Simulation

A 2D vertical numerical model for solving unsteady Navier-Stokes equations with capability of calculating dynamic pressures in free surface flows is used in the present study. In this model, the projection method is applied to solve the equations in non-orthogonal curvilinear coordinate system with collocated grid arrangement. The velocities (fluxes) on cell faces are calculated using a “linear interpolation” method and some “momentum interpolation” methods. These methods are evaluated using some test cases including flow in a trench, flow over a sill and gradually varied flow (M2 profile). The results show that for mild free surface slope, all the momentum interpolation methods implemented in the model have the same accuracy. Also, the linear interpolation of velocity results in an acceptable accuracy. In other words, the checker board pressure fluctuation does not occur in flow domain. For sharp free surface slope, the linear interpolation of velocity causes nonphysical pressure fluctuation and results in divergence. Therefore, the momentum interpolation methods are inevitable. Comparing the required computational time of the methods shows that momentum interpolation methods needs less time in comparison with velocity linear interpolation method. The tests show that evaluating the cell face velocities are more important in longitudinal direction than the vertical ones. Therefore, if the momentum interpolation method is used for east and west faces of cells and the linear interpolation of velocity is used for top and bottom faces, the model runs in less time without reducing the accuracy.