# GAS FLOW IN A SINGLE CYLINDER INTERNAL COMBUSTION ENGINE: A MODEL AND ITS NUMERICAL TREATMENT

GABRIELE ENGL (Mathematisches Institut, Technische Universität München, Arcisstr. 21, Postfach 202420, D‐8000 München 2, Germany)
PETER RENTROP (Mathematisches Institut, Technische Universität München, Arcisstr. 21, Postfach 202420, D‐8000 München 2, Germany)

ISSN: 0961-5539

Article publication date: 1 January 1992

161

## Abstract

We present results of a mathematical model for the gas flow in an internal combustion engine consisting of a single cylinder with an inlet and outlet pipe. In order to achieve optimal performance of the engine the dependence of the gas flow on physical parameters such as pipe dimensions and valve geometry need to be understood. A system of ordinary differential equations (in time t) with discontinuous right‐hand side describes the gas properties in the cylinder, whereas the gas flow in each pipe is modelled by the Euler equations, a system of hyperbolic partial differential equations. The explicit method of Euler and a TVD scheme are used for solving these equations. However, since the coupling of the pipe equations with the o.d.e. system in the cylinder on one side and atmospheric gas properties on the other appeared to be a main problem, we concentrate on appropriate coupling conditions. The numerical techniques involve discretization in space and time, and we present different methods of discrete coupling. As a main result we show that the various coupling methods lead to quite different numerical solutions. Therefore, a careful treatment of the coupling conditions is crucial.

## Citation

ENGL, G. and RENTROP, P. (1992), "GAS FLOW IN A SINGLE CYLINDER INTERNAL COMBUSTION ENGINE: A MODEL AND ITS NUMERICAL TREATMENT", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 2 No. 1, pp. 63-78. https://doi.org/10.1108/eb017480

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