A fast solver for gas flow networks

Abstract

A network formulation is introduced for the modeling and numerical simulation of complex gas transmission systems like a multi-cylinder internal combustion engine. Basic elements of a network are chambers of finite volume, e. g. cylinders of an internal combustion engine, pipes and connections like valves or nozzles. Chamber states are described by ODE systems in time which include measurement results for heat losses and the combustion energy. The pipe now is modeled by the unsteady, one-dimensional Euler equations of gas dynamics. A semi-empirical approach for the connections, which are characterized by throttling effects, yields boundary (coupling) conditions - a system of differential algebraic equations (DAEs) in time. The numerical solution is based on a TVD scheme for the pipe flow and a predictorcorrector method for the remaining DAE system. Different extensions of the TVD method to the inhomogeneous Euler equations are discussed. Simulation results for an internal combustion engine show that a fast solver is obtained for complex gas flow problems which is applied in industrial research.