A scheme for improving computational efficiency of quasi-two-dimensional model

The quasi-2D model, taking into account the axial velocity profile in the cross section and neglecting the convective term in the 2-D equation, can more accurately simulate the water hammer than the 1-D model using the cross-sectional mean velocity. However, as compared with the 1-D model, the quasi-2D model bears a higher computational burden. In order to improve the computational efficiency, the 1-D method is proposed to be used to solve directly the pressure head and the discharge in the quasi-2D model in this paper, based on the fact that the pressure head obtained as the solution of the two-dimensional characteristic equation is identical to that solved by the 1-D characteristic equations. The proposed scheme solves directly the 1-D characteristic equations for the pressure head and the discharge using the MOC and solves the 2-D characteristic equation for the axial velocities in order to calculate the wall shear stress. If the radial velocity is needed, it can be evaluated easily by an explicit equation derived from the explicit 2-D characteristic equation. In the numerical test, the accuracy and the efficiency of the proposed scheme are compared with two existing quasi-two-dimensional models using the MOC. It is shown that the proposed scheme has the same accuracy as the two quasi-2D models, but requires less computational time. Therefore, it is efficient to use the proposed scheme to simulate the 2-D water hammer flows.