1D gas dynamic modelling of mass conservation in engine duct systems with thermal contact discontinuities

A detailed analysis of mass non-conservation in the proximity of thermal contact discontinuities, when solving 1-D gas dynamic flow equations with finite difference numerical methods, is carried out in this paper. A wide spectrum of finite difference numerical methods has been applied to solve such conditions. Thermal contact discontinuities are very common in current diesel engines due to back-flow in the intake valves during the valve overlap period. Every method has been shown to be incapable of correctly solving the problem raised, displaying (or revealing) a different behavior. Taking as base line these analyses a study regarding mesh size reduction in ducts has been also performed. This solution becomes suitable since it leads to making mass conservation problems disappear. Nevertheless, most extended calculation structure in 1D gas dynamic models is not advised due to the increase of computational effort required. Thus, a new calculation structure for solving governing equations in ducts is suggested. This proposed calculation structure is based on independent time discretisation of every duct according to its CFL stability criterion. Its application to thermal contact discontinuities points out its advantages with regard to computational demand as the calculation time of every duct is adapted to its mesh size.