Simulation of transient flow caused by pump failure: Point-Implicit Method of Characteristics

A Point-Implicit Method of Characteristics (PIMOC) and an improved pump formulation are presented in this paper for the efficient simulation of transient flows caused by pump failure. The proposed methods can essentially be considered as modifications to the newly introduced Implicit Method of Characteristics (IMOC) by the authors. The IMOC, however, requires more computational effort than the conventional explicit version due to the fact that IMOC requires the solution of a nonlinear system of equations at each time step. To alleviate this problem, a Point-Implicit version of the IMOC is proposed here which requires less computational effort while enjoying all the advantages of the original IMOC. The proposed method is based on the observation that the assembled equations at each interior point of the pipe segments are uncoupled from those of the other points, including nodal points, which are used to define the system layout. These equations can, therefore, be separately solved for the unknown head and flow at these points before the remaining equations are assembled to form the final system of equations. The solution of the resulting system of equations with a size equal to twice as the number of nodes yields the value of head and flow at the remaining nodal points. To further improve the convergence of the method for the simulation of pump failure, an improved formulation of the pump is also proposed. In the proposed formulation, one of the pump characteristic parameters is also used to formulate the behavior of the pump elements. The proposed Point-Implicit Method and improved pump formulation are used to solve a set of numerical examples and the results are compared with those of original IMOC. For this, the element-wise formulations of two new devices namely junction and check-valve are also introduced. The experiments show improved efficiency of the proposed methods compared to the original IMOC.