A hybrid Broyden family method and its applications in isothermal steady simulation for gas transmission pipeline

The paper presents a hybrid Broyden family method with global mesh refinement and high order discretization scheme because that this type methods are usually efficient and the high order discretization scheme could reduce the discretization error significantly. The method is then applied to pipeline isothermal simulation problems. The method includes the idea of local/global mesh refinement. The mesh refinement is normally used to achieve desired solution accuracy. However, if the coarse mesh is constructed firstly and starting mesh refine at the time that the solution nearly converges to the optimal solution, then this idea would dramatically reduce the computational cost with solution accuracy keeps the same level. Full implementation of mesh refinement requires that the solution point should not be changed during the mesh refinement process. This is done by an interpolation from the previous solution point. The entire process is automatically controlled by the solver with built-in algorithms. Typical applications for pipeline isothermal simulation are given in details and with a field example attached thereafter. The accuracies obtained by different numerical solver are compared. The average error between the proposed method and a commercial software package is around 0.8% for velocity profile. The efficiency of this method is compared with the efficiency of a typical Quasi-Newton method. Numerical tests show that the method saves more than 48% CPU time compared with the efficient methods.