Comparison of Algorithms for Unsteady Flow Calculations in Inlet and Exhaust Systems of IC Engines

Abstract

A comparison of different numerical algorithms used in commercial codes for the calculation of the one-dimensional unsteady flow in the pipes of the inlet and exhaust systems of internal combustion engines is presented in this work. The comparison is made between the Method Of Characteristics (MOC), different Lax-Wendroff schemes, first order upwind schemes and the newest TVD (Total Variation Diminishing) schemes. These algorithms are representative for the complete evolution noticed in the computer codes from the beginning of their use to the present state of the art. Two models of realistic problems in engine simulation tasks are considered: the shock tube calculation (so called Sod’s problem) and the calculation in a tapered pipe. The first test case simulates the exhaust valve opening and releasing a pressure (shock)wave in the exhaust manifold while the other test case covers any gradual variation in the cross section of the manifold pipes. For both test cases computed results are compared with an exact solution and computer time and accuracy are evaluated. None of the examined schemes is completely satisfactory. They either show too much overshoots (for the first test case), or they have local discretization errors (at the section changes of the second test case). A new TVD scheme is proposed that does not introduce any of the foregoing inaccuracies. With this scheme overshoots and dips are eliminated and mass balances are fulfilled, while maintaining high accuracy. [S0742-4795(00)00304-5]