Analysis of time integration methods for the compressible two-fluid model for pipe flow simulations

摘要

In this paper we analyse different time integration methods for the two-fluid model and propose the BDF2 method as the preferred choice to simulate transient compressible multiphase flow in pipelines. Compared to the prevailing Backward Euler method, the BDF2 scheme has a significantly better accuracy (second order) while retaining the important property of unconditional linear stability (A-stability). In addition, it is capable of damping unresolved frequencies such as acoustic waves present in the compressible model (L-stability), opposite to the commonly used Crank-Nicolson method. The stability properties of the two-fluid model and of several discretizations in space and time have been investigated by eigenvalue analysis of the continuous equations, of the semi-discrete equations, and of the fully discrete equations. A method for performing an automatic von Neumann stability analysis is proposed that obtains the growth rate of the discretization methods without requiring symbolic manipulations and that can be applied without detailed knowledge of the source code.