### Computational Simulation of in-Cylinder Flows in Internal Combustion Engines by Means of the Coupling of Zero-/One-Dimensional and Multidimensional Codes

Ezequiel J. López, Norberto M. Nigro

#### Abstract

The computational simulation applied to internal combustion engines is a powerful tool useful for both designing and improving performance. Multidimensional CFD (Computational Fluid Dynamics) codes allow a detailed computation of the flow in the various components of an internal combustion engine, being able to assess the impact of the geometry and the operating conditions. However, due to the high computational cost, it is unviable to simulate all the engine components simultaneously.
On the other hand, the imposition of the boundary conditions in the multidimensional (multi-D) model is not a simple task, because an engine is a dynamic system. In other words, it is necessary to account for the influence of the rest of the system on the part being solved with the multi-D model. Currently, a typical approach is to simulate a specific part of an engine (as, for instance, the combustion chamber, the intake and exhaust ports, etc.) with a CFD multi-D code and the rest of the machine with a 0D/1D (zerodimensional/one-dimensional) engine simulator. Thus, the 0D/1D code provides appropriate boundary conditions for the multidimensional computation. This approach is known as Geometrical Multiscale method and allows a substantial reduction of the numerical complexity. The use of this method leads to the need to couple properly dimensionally heterogeneous models, both in the mathematical formulation
as in the computational implementation. This paper presents some preliminary results of the coupling of CFD 0D/1D and multi-D codes for the realization of in-cylinder flow computations in internal combustion engines. Generally, there are several orders of magnitude of difference between the computational cost of 0D/1D and multi-D models, the latter being the most costly. The implementation proposed in this paper to solve the coupling between codes is based on the difference in computational costs and in the possibility to modify the source codes. Multi-D models are solved using a stabilized finite element
method with an implicit scheme for temporal integration, and the 0D/1D code uses an explicit finite volume method. A subcycling-time-stepping strategy is applied in order to synchronize the simulation in time. Results corresponding to a virtual flowmetry performed on a motored opposed-piston internal combustion engine are presented.

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